CN109257234B - The monitoring and control method of positive negative information coupling diffusion in online community network - Google Patents
The monitoring and control method of positive negative information coupling diffusion in online community network Download PDFInfo
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- CN109257234B CN109257234B CN201811336202.8A CN201811336202A CN109257234B CN 109257234 B CN109257234 B CN 109257234B CN 201811336202 A CN201811336202 A CN 201811336202A CN 109257234 B CN109257234 B CN 109257234B
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
- H04L41/14—Network analysis or design
- H04L41/142—Network analysis or design using statistical or mathematical methods
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
- H04L41/14—Network analysis or design
- H04L41/145—Network analysis or design involving simulating, designing, planning or modelling of a network
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/30—Network architectures or network communication protocols for network security for supporting lawful interception, monitoring or retaining of communications or communication related information
- H04L63/302—Network architectures or network communication protocols for network security for supporting lawful interception, monitoring or retaining of communications or communication related information gathering intelligence information for situation awareness or reconnaissance
Abstract
This disclosure relates to the monitoring method of positive negative information coupling diffusion and the control method of negative information diffusion in a kind of online community network.Wherein, monitoring method is classified different User Status according to whether user receives positive negative information, define transfer relationship of the user between different conditions, and positive negative information coupled diffusion model SPNC is established, utilize the positive negative information coupling diffusion situation in the online community network of the Model Monitoring；The control method of the negative information diffusion proposes the control strategy spread to negative information in network for the user for possessing negative information, to provide support for the control problem that negative information in online community network is spread.
Description
Technical field
This disclosure relates to online community network, expand in particular, being related to positive negative information coupling in a kind of online community network
Scattered monitoring method and the control method of negative information diffusion.
Background technique
With the fast development of Internet technology and mobile terminal device, online community network become a kind of user exchange and
Propagate the Important Platform of viewpoint etc..It is played in people's livelihood fields such as many field instant messagings, medical treatment & health and traffic
Important function.Meanwhile it has also attracted the great interest of many researchers.It is difficult to avoid that, such as Facebook,
Twitter and Sina Weibo etc. greatly changes the communication mode of people in line platform.On the one hand, these are in line platform
The propagation of positive information (news and current affairs, Science Report etc.) brings great convenience, unfortunately, the opening of online community network
Property and diversity are also that the diffusion of negative information (such as rumour and fraud information) creates environment.For example, in March, 2018,
Cambridge Analytica company utilizes from improper 5000 be collected into Facebook in the scandal of Facebook leaking data
The personal data at general-purpose family are propagated to provide data acquisition, analysis and strategy for Ictiobus cyprinllus person participating in the election, are exactly " behaviour briefly
The vertical will of the people ".Therefore, it is unfavorable to the data protection of user to attack Facebook one after another by people from all walks of life, false new by censure communication network
It hears, has misled the user and voter in the U.S..Therewith, it is influenced by this negative press, when the average stop of the upper user of Facebook
Between substantially shrink, Facebook share price on Monday once slumping 8% or more and senior executive generate serious fissure in a party.
Online community network is developing progressively in order to which information is propagated and exchanges indispensable platform.Positive information and negative information
Coupling diffusion to individual and society bring important influence, the diffusion of negative information has become one in online community network
The generally existing phenomenon of kind, however wherein the generally propagation of negative information will cause serious public's uneasiness and social disturbances.Therefore,
How monitoring the motor efficiency of positive negative information and carrying out control to the diffusion of negative information is a challenging job.
Currently, existing research work can inhibit the diffusion of negative information to a certain extent.However, previous research work
The efficiency and negative information for ignoring control strategy are spread loses to system bring.Meanwhile in limited system resources
In the case of, the expense that control strategy is implemented is relatively high.
Therefore, in order to portray the motor efficiency of positive negative information and reduce negative information the diffusion couple network user shadow
It rings, is badly in need of establishing the control method of relevant information monitoring method and negative information diffusion.
Summary of the invention
In view of the above-mentioned problems, the present disclosure proposes a kind of monitoring methods of negative information coupling diffusion positive in online community network
And the method for negative information diffusion control, the monitoring method define state transfer relationship for the user of different conditions in network,
And a positive negative information coupled diffusion model SPNC is established, it is positive and negative in online community network to monitor to be then based on this model
Information coupling diffusion situation, and then corresponding control strategy is proposed for the user for possessing negative information, control strategy can be obtained
Change with time relationship, to control the diffusion of negative information in online community network.
In consideration of it, present disclose provides a kind of monitoring methods of negative information coupling diffusion positive in online community network, including
Following step:
S100, whether positive information or negative information are had received according to user in network, by the user in online community network into
Row state classification:
(1) unknown state S: user had both been not received by positive information, was also not received by negative information；
(2) positive information-diffusion state P: user has been currently received positive information and has approved it, simultaneously participates in the expansion of positive information
It dissipates；
(3) negative information-diffusion state N: user has been currently received negative information and has approved it, simultaneously participates in the expansion of negative information
It dissipates；
(4) double information-chaos state C: user currently possesses positive information and negative information simultaneously, but in state of hovering, the use
Family had both been not involved in the diffusion of positive information, while being also not involved in the diffusion of negative information；
S200, according to the User Status divided in step S100, define the transfer relationship between different conditions:
A) user in state S has received after the positive information of state P user, is transferred to state P with probability α；
User in state S has received after the negative information of state N user, is transferred to state N with probability β；
B) after the user in state P has received the negative information from state N user, state N is transferred to simultaneously with probability γ
And participate in the diffusion of negative information；After user in state P has received positive information and negative information from state C user, with general
Rate δ is transferred to state C；
C) in state N user have received the positive information from state P user after, with probability ε be transferred to state P and
Participate in the diffusion of positive information；After user in state N has received positive information and negative information from state C user, with probability ρ
It is transferred to state C；
D) user in state C has received after the positive information of the user of state P, is transferred to state P with probability λ
And participate in the diffusion of positive information；User in state C receives after the negative information of the user of state N, with probability μ
It is transferred to state N and participates in the diffusion of negative information；
S300 establishes positive negative information coupled diffusion model SPNC according to transfer relationship of the user between different conditions, packet
Containing such as following formula (1)-(5):
S (0) >=0, p (0) >=0, n (0) >=0, c (0) >=0； (5)
Formula (1), (2), (3) and (4) respectively indicates at any time in unknown state S, positive information-diffusion state P, negative letter
User's ratio of breath-diffusion state N and double information-chaos state C change with time relationship, constitute a nonlinear dynamic system,
Formula (5) indicates the primary condition that the SPNC model meets；
In formula, s (t), p (t), n (t), c (t) indicate that the number of users in state S, P, N and C is used always at any time
Shared ratio, has in amount s(t)+p
(t)+c (t)=1+n (t)；Wherein, S (t), P (t), N (t), C (t) indicate that any time t is in the user of S, P, N and C-state
It counting, Φ (t) indicates number of users total in network area Θ at any time, there is S (t)+P (t)+N (t)+C (t)=Φ (t),
And initial value S (0) >=0, P (0) >=0, N (0) >=0, C (0) >=0；S400 utilizes the online community network of SPNC Model Monitoring
In positive negative information coupling diffusion situation.
On the basis of above-mentioned monitoring method, the disclosure additionally provide it is a kind of based on above-mentioned monitoring method to online society
Negative information in network spreads the method controlled, includes the following steps:
For different conditions locating for user, the different control strategies to be implemented are determined；
The control strategy possesses positive information for being converted to user from the current a certain state for possessing negative information
State, to control the diffusion of negative information in a network.
Compared with prior art, the disclosure has following advantageous effects:
(1) whether positive negative information is received according to the user in network and participates in the diffusion of positive negative information, by online social network
User in network has carried out state classification, and user in different states can be according to positive information or the negative information transfer received
To different states, therefore is conducive to the trend of positive negative information coupling diffusion in the online community network of quantitative analysis and and discloses
The complicated feature of positive negative information coupling diffusion；
(2) positive negative information coupled diffusion model SPNC in online community network is established, so that in online community network just
The coupling diffusion trend of negative information is able to accurately portray and monitor.
(3) control strategy proposed for the user of different conditions can change user's ratio in each state, and
And the objective function by establishing system optimization, the optimal control policy for obtaining control negative information diffusion change with time pass
System has reached negative information in the online community network of control and has spread so that the optimum control decision for the diffusion of information that is negative provides foundation
Purpose.
Detailed description of the invention
The schematic diagram of user's transfer relationship between different conditions in Fig. 1 an embodiment of the present disclosure；
Unknown state is in Fig. 2 an embodiment of the present disclosure when critical condition is 0.1294, positive information-diffusion state, is born
User's ratio of information-diffusion state and double information-chaos states changes over time the schematic diagram of relationship；
When critical condition is 0.5 in unknown state, positive information-diffusion state, negative letter in Fig. 3 an embodiment of the present disclosure
User's ratio of breath-diffusion state and double information-chaos states changes over time the schematic diagram of relationship；
Unknown state is in Fig. 4 an embodiment of the present disclosure when critical condition is 0.9188, positive information-diffusion state, is born
User's ratio of information-diffusion state and double information-chaos states changes over time the schematic diagram of relationship；
Unknown state is in Fig. 5 an embodiment of the present disclosure when critical condition is 1.6552, positive information-diffusion state, is born
User's ratio of information-diffusion state and double information-chaos states changes over time the schematic diagram of relationship；
Unknown state is in Fig. 6 an embodiment of the present disclosure when critical condition is 2.8718, positive information-diffusion state, is born
User's ratio of information-diffusion state and double information-chaos states changes over time the schematic diagram of relationship；
When critical condition is 4.5 in unknown state, positive information-diffusion state, negative letter in Fig. 7 an embodiment of the present disclosure
User's ratio of breath-diffusion state and double information-chaos states changes over time the schematic diagram of relationship；
In Fig. 8 an embodiment of the present disclosure in Case 1 unknown state, positive information-diffusion state, negative information-diffusion state and double
Information-chaos state user's ratio changes with time relation schematic diagram；
Positive information-diffusion state, negative information-diffusion state and double information-are mixed in Case 2 in Fig. 9 an embodiment of the present disclosure
User's ratio of ignorant state and two kinds of control strategies change with time relation schematic diagram；
In Figure 10 an embodiment of the present disclosure in Case 3 positive information-diffusion state, negative information-diffusion state and double information-
User's ratio of chaos state and two kinds of control strategies change with time relation schematic diagram；
In Figure 11 an embodiment of the present disclosure in Case 4 positive information-diffusion state, negative information-diffusion state and double information-
User's ratio of chaos state and two kinds of control strategies change with time relation schematic diagram；
In Figure 12 an embodiment of the present disclosure in Case 5 unknown state, positive information-diffusion state, negative information-diffusion state and
User's ratio of double information-chaos states changes over time the schematic diagram of relationship；
In Figure 13 an embodiment of the present disclosure in Case 6 positive information-diffusion state, negative information-diffusion state and double information-
User's ratio of chaos state and two kinds of control strategies change with time relation schematic diagram；
In Figure 14 an embodiment of the present disclosure in Case 7 positive information-diffusion state, negative information-diffusion state and double information-
User's ratio of chaos state and two kinds of control strategies change with time relation schematic diagram；
In Figure 15 an embodiment of the present disclosure in Case 8 positive information-diffusion state, negative information-diffusion state and double information-
User's ratio of chaos state and two kinds of control strategies change with time relation schematic diagram；
Master control expense contrast schematic diagram in Figure 16 an embodiment of the present disclosure in Case1-8.
Specific embodiment
In one embodiment, a kind of monitoring method of positive negative information coupling diffusion in online community network, packet are provided
Include following step:
S100, whether positive information or negative information are had received according to user in network, by the user in online community network into
Row state classification:
(1) unknown state S: user had both been not received by positive information, was also not received by negative information；
(2) positive information-diffusion state P: user has been currently received positive information and has approved it, simultaneously participates in the expansion of positive information
It dissipates；
(3) negative information-diffusion state N: user has been currently received negative information and has approved it, simultaneously participates in the expansion of negative information
It dissipates；
(4) double information-chaos state C: user currently possesses positive information and negative information simultaneously, but in state of hovering, the use
Family had both been not involved in the diffusion of positive information, while being also not involved in the diffusion of negative information；
S200, according to the User Status divided in step S100, define the transfer relationship between different conditions:
A) user in state S has received after the positive information of state P user, is transferred to state P with probability α；
User in state S has received after the negative information of state N user, is transferred to state N with probability β；
B) after the user in state P has received the negative information from state N user, state N is transferred to simultaneously with probability γ
And participate in the diffusion of negative information；After user in state P has received positive information and negative information from state C user, with general
Rate δ is transferred to state C；
C) in state N user have received the positive information from state P user after, with probability ε be transferred to state P and
Participate in the diffusion of positive information；After user in state N has received positive information and negative information from state C user, with probability ρ
It is transferred to state C；
D) user in state C has received after the positive information of the user of state P, is transferred to state P with probability λ
And participate in the diffusion of positive information；User in state C receives after the negative information of the user of state N, with probability μ
It is transferred to state N and participates in the diffusion of negative information；
S300 establishes positive negative information coupled diffusion model SPNC according to transfer relationship of the user between different conditions, packet
Containing such as following formula (1)~(5):
S (0) >=0, p (0) >=0, n (0) >=0, c (0) >=0； (5)
Formula (1), (2), (3) and (4) respectively indicates at any time in unknown state S, positive information-diffusion state P, negative letter
User's ratio of breath-diffusion state N and double information-chaos state C change with time relationship, constitute a nonlinear dynamic system,
Formula (5) indicates the primary condition that the SPNC model meets；
In formula, s (t), p (t), n (t), c (t) indicate that the number of users in state S, P, N and C is used always at any time
Shared ratio, has in amount s(t)+p
(t)+c (t)=1+n (t)；Wherein, S (t), P (t), N (t), C (t) indicate that any time t is in the user of S, P, N and C-state
It counting, Φ (t) indicates number of users total in network area Θ at any time, there is S (t)+P (t)+N (t)+C (t)=Φ (t),
And initial value S (0) >=0, P (0) >=0, N (0) >=0, C (0) >=0；
S400 utilizes the positive negative information coupling diffusion situation in the online community network of SPNC Model Monitoring.
For above-described embodiment, it will be understood that when the user in online community network receives an information, Ta Mentong
Often there is thinking, believe and approve and participate in diffusion three behaviors.It is assumed that have Φ user in the online community network Θ of homogeneity,
And information can be interacted and propagated between user.When positive information and negative information are propagated in network Θ, we are according to user
Receive the different situations of positive negative information, such as whether user has been received positive negative information, user whether believe positive negative information and
User in network is divided into four kinds of states, i.e. step S100:(1 by several situations of diffusion whether user participates in positive negative information)
Unknown state S: user had both been not received by positive information, was also not received by negative information；(2) positive information-diffusion state P: user is current
It has received positive information and approves it, simultaneously participate in the diffusion of positive information；(3) negative information-diffusion state N: user currently receives
It has arrived negative information and has approved it, simultaneously participated in the diffusion of negative information；(4) double information-chaos state C: user is currently owned by positive letter
Breath and negative information, and in state of hovering, which had both been not involved in the diffusion of positive information, while being also not involved in the expansion of negative information
It dissipates.Simultaneously, it is believed that any one of network user belongs to one of above-mentioned four kinds of states at any time.
Then our as follows, i.e. step S200 that define the metastasis between different conditions:
Positive information is neither received when a user is in state S nor receives negative information.Therefore, if one is in shape
The user of state S has received after the positive information of state P user, it will is transferred to state P with probability α；Else if one
User in state S has received the negative information from state N user, it will is transferred to state N with probability β.
When a user is in positive information-diffusion state P, which possesses at present and believes positive information, while can join
With the diffusion of positive information.Therefore, if the user has received the negative information from state N user, shape will be transferred to probability γ
State N and the diffusion for participating in negative information；Otherwise the user will be transferred to state C with probability δ.
When a user is in negative information-diffusion state N, which is currently owned by and approves negative information, while can join
With the diffusion of negative information.Therefore, when a user receives the positive information from state P user, state will be transferred to probability ε
P and the diffusion for participating in positive information；Otherwise the user will be transferred to state C with probability ρ.
When a user is in double information-chaos state C, which possesses positive information and negative information and simultaneously in shape of hovering
State.If a user of the state receives the positive information of the user from state P, he will be transferred to shape with probability λ
State P and the diffusion for participating in positive information；Or a user of the state receives the negative information of the user from state N,
He will be transferred to state N with probability μ and participate in the diffusion of negative information.
In view of the social activities of user, it is assumed that the user in network can leave region Θ any time with probability θ.
Meanwhile there is ω user to enter region Θ from the outside at any time, and it is assumed that from the outside into network area Θ's
User will be in state S, the major parameter used in following state metastasis such as table 1.
Major parameter in 1. dynamic model of table
In the disclosure, with S (t), P (t), N (t), C (t) Lai Daibiao any time is in the number of users of S, P, N and C-state,
Number of users total in network area Θ at any time, i.e. S (t)+P (t)+N (t)+C (t)=Φ (t) are indicated with Φ (t).
According to above-mentioned state metastasis, available following state transfer relationship is as shown in Figure 1.
In Fig. 1 in the meaning of parameters such as table 1, while θ S, θ P, θ N, θ C indicates to be in S, the user of P, N and C-state
Leave the total number of region Θ；WithIndicate the user in state S respectively with probability α0And β0It is transferred to state
The number of users of P and N isWith WithIndicate the user in state P respectively with probability γ0And δ0It is transferred to
The number of users of state N and C isWith WithIndicate the user in state N respectively with probability ε0And ρ0
The number of users for being transferred to state P and C isWith WithIndicate the user in state C respectively with probability λ0
And μ0The number of users for being transferred to state P and N isWith
Next, needing to model negative information coupling diffusion positive in network, i.e. step S300, the SPNC finally established
Model are as follows:
S (0) >=0, p (0) >=0, n (0) >=0, c (0) >=0. (5)
Foundation is specifically described below and obtains the process of the model.
Firstly, according to transfer relationship of the user between different conditions, using S according to the state metastasis of above-mentioned elaboration
(t), P (t), N (t), C (t) Lai Daibiao any time are in the number of users of S, P, N and C-state, establish about number of users at any time
Between the kinetics equation that changes:
Formula (6), (7), (8) and (9) respectively indicates at any time in unknown state S, positive information-diffusion state P, negative letter
User's number of breath-diffusion state N and double information-chaos state C change with time relationship:
It is apparent that formula (6)-(9) constitute a nonlinear dynamical system, it has following initial value:
S (0) >=0, P (0) >=0, N (0) >=0, C (0) >=0 (10) formula (10) indicates to be in unknown state S, positive information-expansion
It dissipates state P, the number of negative information-diffusion state N and double information-chaos state C user in the initial state and is both greater than equal to 0.
In the dynamic model, the changing rule of total number of users is expressed as follows in the Θ of network area:
Formula (11) indicates the relationship that total user's number in the Θ of network area changes over time.
That is Φ (t) is changing with the time, and
In addition, allowingIt can find s (t), p (t),
N (t), c (t) indicate the ratio shared in total number of users in the number of users of state S, P, N and C, wherein s (t)+p (t)+n (t)+
C (t)=1.Allow τ=θ t simultaneously, It is very easy to find s (t), p (t), n (t), c (t) meets the following differential equation:
Formula (1), (2), (3) and (4) respectively indicates at any time in unknown state S, positive information-diffusion state P, negative letter
User's ratio of breath-diffusion state N and double information-chaos state C change with time relationship.Simultaneously (1)-(4) constitute one it is non-
Linear dynamic system, the positive negative information coupled diffusion model SPNC as established.The model meets following initial strip simultaneously
Part:
S (0) >=0, p (0) >=0, n (0) >=0, c (0) >=0 (5)
Formula (5) indicates to be in unknown state S, positive information-diffusion state P, negative information-diffusion state N and double information-chaos state C
User's ratio is more than or equal to 0 in an initial condition.
Then, the coupling of the positive negative information in online community network can be monitored using the established SPNC model to expand
Dissipate situation.The positive and negative diffusion of information situation obtained according to monitoring, so that it may further the diffusion of information in online network be taken
Corresponding control strategy.
In one embodiment, further include following step after establishing above-mentioned SPNC model:
According to transfer relationship of the user between each state, the critical condition that negative information is spread in a network is determined:
Wherein R0Whether continue the critical condition spread in a network for negative information；If R0Negative information less than 1, in network
It is automatic to disappear, it does not continue to spread；If R0Greater than 1, the negative information in network is spread in a network with stable tendency continuation.
In this embodiment, in order to illustrate critical condition is determined, the concept of equalization point is introduced.
If each differential equation (1)-(4) value is equal to 0 to all time t, system, which will be in, stablizes shape
State has at this time:
Formula (12) indicates unknown state S, positive information-diffusion state P, negative information-diffusion state N and double information-chaos state C user
Ratio change with time rate be 0, i.e. system has reached an equilibrium state.
By solving formula (12), the zero balancing point E of the available model0(1,0,0,0) and Positive balance point E*(s*, p*,
n*, c*)；
WhereinAnd
a1=β (δ+ε-γ-λ), a2=α (δ+ε-γ-λ)+β (δ-λ), a3=(δ+ε-γ-λ)+β (λ-δ -1), a4=α
(λ-δ), a5=λ-δ -1, a6=α -1.
It follows that the trend of diffusion of information can be there are two types of situation, system is stablized in zero balancing point E in the case of the first0
(1,0,0,0) does not have the user of negative information-diffusion state user and double information-chaos states at this time in network, only place does unknown
The user of state: system stabilization deposits Positive balance point E in another case*(s*, p*, n*, c*), the user of four kinds of states exists at this time
And quantity keeps stablizing.
Positive negative information coupled diffusion model based on above-mentioned foundation can determine negative information in net by further analyzing
The critical condition spread in network, so that the implementation for control strategy provides decision-making foundation.
If K=(c, n, p, s)T, then the differential equation (1)-(4) can be rewritten asWherein:
Formula (13) indicates the user influenced by negative information in double information-chaos state C, negative information-diffusion state N, positive information-
The ratio that state P and unknown state S occurs is spread, every a line has respectively corresponded unknown state S, positive information-diffusion to the matrix from top to bottom
State P, negative information-diffusion state N and double information-corresponding ratio of these four states of chaos state C.
Formula (14) is indicated in double information-chaos state C, negative information-diffusion state N, unknown state S and positive information-diffusion state P
The change rate of user's ratio, the top-down every a line of the matrix respectively correspond unknown state S, positive information-diffusion state P, negative letter
Breath-diffusion state N and double these four corresponding states of information-chaos state C.
The state for possessing negative information in four kinds of different states is N and C, SPNC model n in equalization point0=c0=0 and
There is K0=(0,0,0,1)T, indicate in double information-chaos state C, negative information-diffusion state N, positive information-diffusion state P and unknown state
User's ratio be 0,0,0,1 respectively.Therefore the front two row of f (X) and v (X) respectively to negative information-diffusion state N and double information-
Chaos state C derivation obtainsTherefore available negative information is in a network
The critical condition of diffusion: R0=ρ (FV-1), wherein ρ (FV-1) it is matrix F V-1Spectral radius:
Wherein ρ ' (FV-1) it is matrix F V-1Spectral radius, R0Namely regenerated Spectral radius radius, it be also negative information whether
The critical condition propagated in a network.Foregoing describe R0Determine whether negative information continues to propagate in a network, therefore, it with
The zero balancing point of SPNC model and the stability of Positive balance point are closely related.
The critical condition spread in a network by determining negative information, available following conclusions are the implementation of control strategy
Decision-making foundation is provided:
Conclusion 1: if R0Less than 1, the user for possessing negative information is become zero, and the negative information in network disappears automatically, no longer
Continue to spread；
Conclusion 2: if R0Greater than 1, unknown state, positive information-diffusion state, negative information-diffusion state and double information-are in network
The user of chaos state exists and ratio keeps stablizing, and the negative information in network is expanded in a network at this time with stable tendency continuation
It dissipates.
It is all taken corresponding whether no matter negative information disappears in view of negative information is spread to influence caused by the network user
Control strategy, it is different according to user state in which, take different control strategies, the control strategy for make user from
The current a certain state for possessing negative information is converted to the state for possessing positive information, to control the diffusion of negative information in a network.
The monitoring method and negative information of positive negative information coupling diffusion in online community network are illustrated in embodiment above-mentioned
The critical condition propagated in a network then illustrates to spread the method controlled to the negative information in online community network.
In one embodiment, the diffusion of the negative information in online community network is controlled based on above-mentioned monitoring method
The method of system, includes the following steps:
For different conditions locating for user, the different control strategies to be implemented are determined；
The control strategy possesses positive information for being converted to user from the current a certain state for possessing negative information
State, then participates in the diffusion of positive information, to control the purpose that negative information is spread in a network.
In one embodiment, the control strategy includes:
Control strategy is treated, for making user from negative information-diffusion state N with probabilityIt is transferred to positive information-diffusion state P；
Control strategy is persuaded, for making user be transferred to positive information-diffusion state P from double information-chaos state C with probability σ.
The Dynamic Evolution of positive negative information coupling diffusion is foregoing described, main target is to implement effective control plan
The influence of user in diffusion couple network slightly to minimize negative information, while minimizing loss and the control overhead of system.The reality
It applies in example and designs two kinds of coordination control strategies for the user of negative information-diffusion state user and double information-chaos states, this strategy
User can be changed in the ratio of different conditions, to realize the purpose of control negative information diffusion.Diffusion for negative information mentions
Two kinds of effective control strategies are specific as follows out:
Treatment: disappearing in negative information-diffusion state users from networks to allow, and has issued the official of positive information either authority
Square information is now in negative information-diffusion state user and believes the negative information received and no longer with probabilityIt is transferred to just
Information-diffusion state participates in the diffusion of positive information, and this treatment control strategy relationship of changing with time is expressed as μ1(t)。
It persuades: and the user in double information-chaos states carries out positive communication exchange, then tells their negative informations certain
It propagates in a network.However, having controlled the diffusion of negative information in network by taking effective control strategy.Then,
User in double information-chaos states will no longer believe negative information and be transferred to positive information-diffusion state with probability σ, join simultaneously
With the diffusion of positive information.This control strategy relationship of changing with time of persuading is expressed as μ2(t)。
In one embodiment, it is lost caused by being spread based on control overhead caused by implementation control strategy, negative information
With positive diffusion of information bring income, determine about the overhead function for implementing control strategy；Determine so that overhead function most
Small control strategy, obtains optimal control policy.
Specifically, system loss and positive information caused by the overhead of two kinds of control strategies of implementation, negative information are spread
Objective function of the bring system benefit as system optimization is spread, the diffusion problem of control negative information is finally converted into one
The smallest optimal control problem of expense is sought, the two of the negative information that is under control in the case where guaranteeing the lesser situation of system overhead diffusion
Kind coordination control strategy, they are able to suppress the diffusion of negative information and the number of users that negative information is influenced is less.
In one embodiment, the overhead function is determined by following formula:
In formula:
J is that total rise is sold；
T is the implementation duration of control strategy；
S (t) indicates the ratio shared in total number of users of the user in unknown state S；
P (t) indicates the ratio shared in total number of users in positive information-diffusion state P user；
N (t) indicates the ratio shared in total number of users in negative information-diffusion state N user；
μ1(t) indicate that treatment control strategy changes with time relationship；
μ2(t) indicate that persuading control strategy changes with time relationship；
W and z is normal number, and wn (t) indicates to be in the loss caused by user security risk of negative information-diffusion state, zp (t) and zs (t)
Indicate the user's bring income for being in positive information-diffusion state and unknown state；
X is normal number, indicates average overhead caused by treatment one negative information-diffusion state user；
Y is normal number, indicates to persuade average overhead caused by the user of a double information-chaos states.
It is described as follows: according to two kinds of coordination control strategies mentioned above, available following improved-
SPNC model:
Formula (17)-(20) respectively indicate any time unknown state S, positive information-diffusion state P, negative information-diffusion state N and double
Information-chaos state C user's ratio changes with time relationship,It indicates to implement control strategy μ1(t) it is in after
Negative information-diffusion state N user is transferred to positive information-diffusion state P user's ratio, whereinIndicate that user shifts from state N
To the probability of state P, μ1(t) indicate that the implementation intensity of the control strategy changes with time relationship, n (t) indicates to be in state N
User's ratio.σμ2(t) c (t) indicates to implement control strategy μ2(t) user afterwards in double information-chaos state C is transferred to positive letter
Breath-diffusion state P, wherein σ indicates that user is transferred to the probability of state P, μ from state C2(t) indicate that the implementation of the control strategy is strong
The relationship that changes with time is spent, c (t) indicates the user's ratio for being in state C.
0, p (0) >=0, the n (0) >=0 of the improved-SPNC model and SPNC model initial value s (0) having the same,
C (0) >=0, while two kinds of control strategy μ1(t) and μ2(t) there is following boundary condition:
0≤μ1(t)≤μ1max, 0≤μ2(t)≤μ2max (21)
Wherein μ1maxAnd μ2maxRespectively represent control strategy μ1(t) and μ2(t) the upper bound, and 0≤μ1max≤ 1,0≤μ2max
≤1。
It is assumed that the expense for implementing two kinds of control strategies is chi square function respectivelyWithIn addition, negative letter
Ratio shared by breath-diffusion state user is spread as negative information loses wn (t) to system bring, and positive information-expansion
Ratio shared by the user of state and the user of double information-chaos states is dissipated as system benefit zp (t) and zs (t) simultaneously, with x and y
It indicates treatment one negative information-diffusion state user within the desired time [0, T] respectively and persuades a double information-chaos
The average overhead that the user of state is spent, therefore, the system goal function that can be defined as follows:
In formula (16)
J is overhead；
T is the implementation duration of control strategy；
S (t) indicates the ratio shared in total number of users of the user in unknown state S；
P (t) indicates the ratio shared in total number of users in positive information-diffusion state P user；
N (t) indicates the ratio shared in total number of users in negative information-diffusion state N user；
μ1(t) indicate that treatment control strategy changes with time relationship；
μ2(t) indicate that persuading control strategy changes with time relationship；
W and z is normal number, and wn (t) indicates to be in the loss caused by user security risk of negative information-diffusion state, zp (t) and zs (t)
Indicate the user's bring income for being in positive information-diffusion state and unknown state；
X is normal number, indicates average overhead caused by treatment one negative information-diffusion state user；
Y is normal number, indicates to persuade average overhead caused by the user of a double information-chaos states.
In one embodiment, the optimal control policy when overhead function obtains minimum value is determined by following formula:
In formula:
Indicate optimal treatment control strategy；
It indicates optimal and persuades control strategy；
μ1maxIndicate μ1(t) the upper bound, μ1(t) indicate that treatment control strategy changes with time relationship；
μ2maxIndicate μ2(t) the upper bound, μ2(t) indicate that persuading control strategy changes with time relationship；
h1Treatment control strategy when to make overhead obtain minimum value；
h2Control strategy is persuaded when to make overhead obtain minimum value.
Specifically, the final goal of system optimization is the control overhead of minimum system and the diffusion couple network of negative information
The influence of middle user, therefore, the formalization representation of the optimal control problem are as follows:
By formula (22) the smallest system control overhead can be found in the hope of the minimum value of system goal function.WhereinWithIndicate optimal control strategy.
Wherein Δ={ μ1(t), μ2(t)|0≤μ1(t)≤μ1max, 0≤μ2(t)≤μ2max}。
In the embodiment, in order to seek optimal control solutionWithAnd system is in optimal control solutionWithCorresponding optimal system state variable s down*(t), p*(t), n*(t), c*(t).Firstly, one Lagrangian letter of construction
L is counted to seek the optimal solution of optimal control problem (22):
In order to acquire Lagrangian functional minimum value, its Hamiltonian letter is defined to the optimal control problem
Number H such as following formula:
Wherein λs(t), λp(t), λn(t), λcIt (t) is adjoint function, next formula (17)-(20)/and formula (23)
It is updated in formula (24), available such as following formula:
Next, seeking the optimal control solution of optimal control problem (22) using the Pontryagin maximum principle.
It is assumed that
, the set that Φ expression is made of optimal state variable, optimal control strategy and optimal adjoint function, thus
It there will necessarily be outstanding vector function λ (t)={ λs(t), λp(t), λn(t), λc(t) } meet following condition:
Wherein q (t) ∈ { s (t), p (t), n (t), c (t) }, correspondingly, q*(t)∈{s*(t), p*(t), n*(t), c*
(t)}.Meanwhile r (t) ∈ { μ1(t), μ2(t) }, thus
Allow s*(t), p*(t), n*(t), c*(t) it is and optimum control variableWithRelevant optimum state
Solution, thus there will necessarily be adjoint functionMeet:
As t=T, there is transversality condition:
Since Hamiltonian function H is about μ1(t) and μ2(t) Square Convex Function, therefore the minimum value of function H exists
At stationary point (i.e.With) obtain, following equation is obtained according to formula (28):
It considersWithBoundary condition, we are it is hereby achieved that optimal control policyWithChange with time relationship:
Wherein And t is time parameter,WithIndicate optimal control
System strategy；μ1maxIndicate control strategy μ1(t) the upper bound, μ2maxIndicate control strategy μ2(t) the upper bound.
ThenWithExpression be rewritten as following formula:
In one embodiment, based on improved-SPNC model, optimum treatment control strategy and optimal control plan is persuaded
Optimal control system is slightly established, the optimal control system is as follows::
Formula (40)-(43) show that optimal system mode changes with time relationship；
In formula,Indicate the probability that user shifts after therapeutic strategy is implemented；
The probability of user's transfer after strategy implement is persuaded in σ expression；
Below by the validity and stabilization of the positive negative information coupled diffusion model proposed in emulation experiment verifying present case
Property analysis correctness.
The major parameter setting such as table 2 used in emulation experiment.
Table 2: the basic parameter in emulation
In order to verify the validity of SPNC model and the correctness of stability analysis, experiment is divided into two kinds of situations to discuss
The stability of zero balancing point and Positive balance point, i.e. R0< 1 and R0> 1.
Work as R0When < 1, three groups of experiments are set to observe the stability of zero balancing point, the parameter setting in three groups of experiments is distinguished
As follows, experimental result is as in Figure 2-4:
α=0.09, β=0.14, ε=0.9, λ=0.9, γ=0.49, δ=0.99, ρ=0.28, μ=0.66；I.e.
α=0.09, β=0.4, ε=0.9, λ=0.9, γ=0.09, δ=0.99, ρ=0.8, μ=0.6；I.e.
α=0.09, β=0.6, ε=0.9, λ=0.9, γ=0.09, δ=0.99, ρ=0.98, μ=0.6；I.e.
Correspondingly, work as R0When > 1, three groups of experiments are set to observe the stability of Positive balance point, the parameter in three groups of experiments is set
Set the following experimental result of difference as illustrated in figs. 5-7:
α=0.69, β=0.96, ε=0.1, λ=0.84, γ=0.85, δ=0.02, ρ=0.48, μ=0.16；I.e.
α=0.69, β=0.89, ε=0.1, λ=0.84, γ=0.85, δ=0.02, ρ=0.88, μ=0.56；I.e.
α=0.69, β=0.96, ε=0.1, λ=0.84, γ=0.85, δ=0.02, ρ=0.68, μ=0.36；I.e.
It is learnt from Fig. 2-4Work as R0When reduction, when system reaches required by zero balancing point
Between it is shorter, the negative information in network will be disappeared with the shorter time, such as negative information-diffusion state N user in Fig. 2,3 and Fig. 4
The time that ratio becomes zero is respectively 40min, 50min and 60min.Meanwhile in R0In the case where < 1, the user in state N
Then quantity, which first increases, quickly to be reduced, and the number of users in state C is also quickly being reduced.After a while, it is
There was only two kinds of user (S and P) in system, negative information will not continue to spread in a network.
It is learnt from Fig. 5-7Work as R0When increase, system reaches required by Positive balance point
Time is shorter, and the negative information in network will continue to exist, i.e., as in Fig. 5,6 and 7, after a while, is in negative letter
Breath-diffusion state N user's ratio and user's ratio of double information-chaos state C tend towards stability value, no longer change.In R0The feelings of > 1
Under condition, the number of users in state N first increases, and then slowly reduces until tending towards stability.After a while, it is in
S, the user of P, N and C-state can exist in systems, and the number of users of these four states gradually tends towards stability.The result is that
Negative information is persistently spread in a network, while certain influence is generated to the user in network.It is above-mentioned the experimental results showed that R0's
Value can reveal that the change procedure of different conditions number of users, this is consistent with the conclusion of SPNC model stability analysis.
Control strategy presented herein is verified below by emulation experiment.
It observes in the case where different control strategies is implemented, positive information-diffusion state in the diffusion couple network of negative information
User's bring of user, negative information-diffusion state user and double information-chaos states influence, and compare under following situations and be
The master control expense of system.Case1-4 is observed at parameter 1 (Parameters-1)；It is observed at parameter 2 (Parameters-2)
Case 5-8。
Parameters-1:
α=0.09, β=0.14, ε=0.9, λ=0.9, γ=0.49, δ=0.99, ρ=0.28, μ=0.66
Case 1:Parameters-1, μ1(t)=0, μ2(t)=0；
Case 2:Parameters-1, μ1(t) ≠ 0, μ2(t)≠0；
Case 3:Parameters-1, μ1(t) ≠ 0, μ2(t)=0；
Case 4:Parameters-1, μ1(t)=0, μ2(t)≠0；
Parameters-2:
α=0.1, β=0.64, ε=0.8, λ=0.9, γ=0.99, δ=0.02, ρ=0.18, μ=0.36
Case 5:Parameters-2, μ1(t)=0, μ2(t)=0；
Case 6:Parameters-2, μ1(t) ≠ 0, μ2(t)≠0；
Case 7:Parameters-2, μ1(t) ≠ 0, μ2(t)=0；
Case 8:Parameters-2, μ1(t)=0, μ2(t)≠0；
In figures 8-11, the corresponding experimental result of Case 5-8 is the corresponding experimental result of Case 1-4 in Figure 12-15
The master control expense of system is in Figure 16.
Case l. has found no any control strategy, i.e. μ from Fig. 81(t) and μ2(t) value is equal to 0.Negative information-diffusion
User's ratio of state, which first increases, reaches its peak value, then quickly reduces, and the peak value of negative information-diffusion state user's ratio reaches
To higher horizontal (about 46%).Meanwhile negative information-diffusion state user's ratio becomes 0 in 40 chronomeres.
In the case where there is control strategy implementation, finds from Fig. 9, in two kinds of control strategies (treat and persuade) while implementing
In the case where, i.e. μ1(t) and μ2(t) value is all not equal to 0.Negative information-diffusion state user's ratio is substantially reduced, and and
Case 1 is compared, and user's ratio peak value achieved that negative information spreads state is smaller (about 23%).Meanwhile the duration of peak value
Be significantly less than the duration of peak value in Case 1, this Experimental comparison results show it is proposed that coordination control strategy controlling
It is very effective in the propagation of negative information processed.
It is found from Figure 10, in the case where a kind of only control strategy is implemented, i.e. μ1(t) it is not equal to 0 and μ2(t) it is equal to 0.
The peak value that negative information-diffusion state user's ratio reaches is relatively small (about 26%).
It finds from Figure 11, compares in the case where only persuading a kind of control strategy and implementing with Case 1, negative information-
The peak value that user's ratio of diffusion state reaches is relatively low (about 31%).
The notable difference of Case 2, Case 3 and Case 4 are continuing for Case 3 and peak value in Case 4 and peak value
Time will be apparently higher than the duration of peak value and peak value in Case 2.Generally, in Case 2, Case 3 and Case4 just
Information-diffusion state user's ratio tend towards stability and user's ratio of double information-chaos states tend to 0 required by the time (about 20
A chronomere) it is more shorter than Case 1 (about 40 chronomeres).The two kinds of collaborations control proposed from the experimental result discovery disclosure
The propagation of policy control negative information processed is most efficient and its control effect will be markedly superior to the control of single control strategy
Effect.
Case 5. has found that two kinds of control strategies (treat and persuade) are not all implemented from Figure 12.Negative information-diffusion state
User's ratio, which increases to, reaches its peak value, then slowly smaller, it is final until tend towards stability (about 38%) shared 40 times
Unit.Meanwhile negative information-diffusion state user's ratio is relatively high (about 48%), positive information-diffusion state user's ratio and double
Information-chaos state user ratio tends towards stability in 40 chronomeres.
In the case where there is control strategy implementation (Case 13-15), find to implement simultaneously in two kinds of control strategies from Figure 13
In the case where (Case 6), i.e., and μ2(t) value is all not equal to 0.Negative information-diffusion state user's ratio is clearly reduced,
And it compares with Case 5, the peak value reached is relatively low (about 21).Meanwhile the duration of peak value is also significantly
Less than the duration of peak value in Case 5.Importantly, its maintenance level also tends to a low-down value (about 0.03),
This contrast and experiment shows that the diffusion of negative information in online community network is effectively controlled, and the collaboration control that the disclosure proposes
Making mechanism is very efficient.
It ought only be treated in the case that a kind of this control strategy implemented in Case 14 from Fig. 9 discovery, i.e. μ1(t) etc.
In 0, μ2(t) when being equal to 0, negative information-diffusion state user's ratio reaches a relatively low level (about 0.22).From Figure 15
It was found that working as μ1(t) it is equal to 0, μ2(t) not equal to when in the case where 0, i.e., only persuading a kind of this control strategy and being carried out, negative information-
User's ratio of diffusion state reaches 35%, and gradually tends towards stability (about 27%).Case 6, Case 7 and Case's 8 is obvious
Difference is that the peak value of Case 6, the duration of peak value and the maintenance level that finally reaches all are the smallest.It moreover has been found that
User's ratio of positive information-diffusion state is apparently higher than the ratio in Case 5, and double letters in Case 6, Case 7 and Case 8
Breath-chaos state user's ratio is significantly lower than the ratio in Case 5.It is eventually found when to system implementation optimal control policy
When, the diffusion of negative information can be effectively suppressed in online community network (OSNs).However, the Collaborative Control plan that the disclosure proposes
Slightly more effective and its control effect is substantially better than the control effect of single control strategy.
The master control expense of system there are apparent difference, always open by the system of Case 5-8 from Figure 16 discovery Case 1-8
Pin is apparently higher than the overhead of system in Case 1-4.Meanwhile being compared with other situations in Parameters-1, Case's 1
Control overhead is highest, and is compared with other situations in Parameters-2, and the control overhead of Case 5 is highest.
Importantly, the case where two kinds of control strategies are implemented simultaneously in Parameters-1 and Parameters-2 (2 He of Case
Case 6) under control overhead be minimum.Therefore, it can be deduced that concurrency controlling mechanism presented herein can make to implement control
The system overhead of strategy is minimum.
Although embodiment of the present invention is described in conjunction with attached drawing above, the invention is not limited to above-mentioned
Specific embodiments and applications field, above-mentioned specific embodiment are only schematical, directiveness, rather than restricted
's.Those skilled in the art are under the enlightenment of this specification and in the range for not departing from the claims in the present invention and being protected
In the case where, a variety of forms can also be made, these belong to the column of protection of the invention.
Claims (9)
1. the monitoring method of positive negative information coupling diffusion, includes the following steps: in a kind of online community network
S100, whether positive information or negative information are had received according to user in network, the user in online community network is subjected to shape
State classification:
(1) unknown state S: user had both been not received by positive information, was also not received by negative information；
(2) positive information-diffusion state P: user has been currently received positive information and has approved it, simultaneously participates in the diffusion of positive information；
(3) negative information-diffusion state N: user has been currently received negative information and has approved it, simultaneously participates in the diffusion of negative information；
(4) double information-chaos state C: user currently possesses positive information and negative information simultaneously, but in state of hovering, the user was both
It is not involved in the diffusion of positive information, while being also not involved in the diffusion of negative information；
S200, according to the User Status divided in step S100, define the transfer relationship between different conditions:
A) user in state S has received after the positive information of state P user, is transferred to state P with probability α；It is in
The user of state S has received after the negative information of state N user, is transferred to state N with probability β；
B) after the user in state P has received the negative information from state N user, state N is transferred to probability γ and is joined
With the diffusion of negative information；After user in state P has received positive information and negative information from state C user, turned with probability δ
Move on to state C；
C) after the user in state N has received the positive information from state P user, state P is transferred to probability ε and is participated in
The diffusion of positive information；After user in state N has received positive information and negative information from state C user, with probability ρ transfer
To state C；
D) had received after the positive information of the user of state P in the user of state C, with probability λ be transferred to state P and
Participate in the diffusion of positive information；User in state C receives after the negative information of the user of state N, with probability μ transfer
To state N and participate in the diffusion of negative information；
S300 establishes positive negative information coupled diffusion model SPNC according to transfer relationship of the user between different conditions, comprising such as
Following formula (1)-(5):
S (0) >=0, p (0) >=0, n (0) >=0, c (0) >=0； (5)
Formula (1), (2), (3) and (4) respectively indicates at any time in unknown state S, positive information-diffusion state P, negative information-expansion
The user's ratio for dissipating state N and double information-chaos state C changes with time relationship, constitutes a nonlinear dynamic system, formula (5)
Indicate the primary condition that the SPNC model meets；
In formula, s (t), p (t), n (t), c (t) indicate that the number of users in state S, P, N and C is in total number of users at any time
In shared ratio, haves(t)+p(t)+n(t)+c(t)
=1；Wherein, S (t), P (t), N (t), C (t) indicate that any time t is in the number of users of S, P, N and C-state, and Φ (t) is indicated
Total number of users in any time network area Θ, there is S (t)+P (t)+N (t)+C (t)=Φ (t), and initial value S (0) >=
0, P (0) >=0, N (0) >=0, C (0) >=0；
S400 utilizes the positive negative information coupling diffusion situation in the online community network of SPNC Model Monitoring.
2. according to the method described in claim 1, further including following step after the step S300:
According to transfer relationship of the user between each state, the critical condition that negative information is spread in a network is determined:
Wherein R0Whether continue the critical condition spread in a network for negative information；
If R0Less than 1, the negative information in network disappears automatically, does not continue to spread；
If R0Greater than 1, the negative information in network is spread in a network with stable tendency continuation.
3. a kind of spread the side controlled based on the monitoring method of claims 1 or 2 to the negative information in online community network
Method includes the following steps:
For different conditions locating for user, the different control strategies to be implemented are determined；
The control strategy is used to that user to be made to be converted to the state for possessing positive information from the current a certain state for possessing negative information,
To control the diffusion of negative information in a network.
4. method according to claim 3, wherein the control strategy includes:
Control strategy is treated, for making user from negative information-diffusion state N with probabilityIt is transferred to positive information-diffusion state P；
Control strategy is persuaded, for making user be transferred to positive information-diffusion state P from double information-chaos state C with probability σ.
5. according to the method described in claim 3, further including following steps:
Loss caused by being spread based on expense caused by implementation control strategy, negative information and positive diffusion of information bring income,
It determines about the overhead function for implementing control strategy；
It determines so that the smallest control strategy of overhead function, to obtain optimal control policy.
6. according to the method described in claim 5, the overhead function is determined by following formula:
In formula:
J is overhead；
T is the implementation duration of control strategy；
S (t) indicates the ratio shared in total number of users of the user in unknown state S；
P (t) indicates the ratio shared in total number of users in positive information-diffusion state P user；
N (t) indicates the ratio shared in total number of users in negative information-diffusion state N user；
μ1(t) indicate that treatment control strategy changes with time relationship；
μ2(t) indicate that persuading control strategy changes with time relationship；
W and z is normal number, and wn (t) indicates to be in the loss caused by user security risk of negative information-diffusion state, and zp (t) and zs (t) are indicated
User's bring income in positive information-diffusion state and unknown state；
X is normal number, indicates average overhead caused by treatment one negative information-diffusion state user；
Y is normal number, indicates to persuade average overhead caused by the user of a double information-chaos states.
7. method according to claim 5 or 6, the optimal control policy when overhead function obtains minimum value is under
Formula determines:
In formula:
Indicate optimal treatment control strategy；
It indicates optimal and persuades control strategy；
μ1maxIndicate μ1(t) the upper bound, μ1(t) indicate that treatment control strategy changes with time relationship；
μ2maxIndicate μ2(t) the upper bound, μ2(t) indicate that persuading control strategy changes with time relationship；
h1Treatment control strategy when to make overhead obtain minimum value；
h2Control strategy is persuaded when to make overhead obtain minimum value.
8. according to the method described in claim 7, wherein, being established based on optimum treatment control strategy and optimal control strategy of persuading
Optimal control system, the optimal control system include following formula (40)-(43):
Formula (40)-(43) indicate that optimal system mode changes with time relationship,
In formula,Indicate the probability that user shifts after therapeutic strategy is implemented；The probability of user's transfer after strategy implement is persuaded in σ expression.
9. according to the method described in claim 8, wherein:
The optimal control system has such as downstream condition: 0≤μ1(t)≤μ1max, 0≤μ2(t)≤μ2max；
Wherein, μ1maxAnd μ2maxRespectively represent control strategy μ1(t) and μ2(t) the upper bound, and 0≤μ1max≤ 1,0≤μ2max≤
1。
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