CN111757461B - Cellular automaton-based annular WSN pulse coupled oscillator time synchronization model - Google Patents
Cellular automaton-based annular WSN pulse coupled oscillator time synchronization model Download PDFInfo
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Abstract
The invention discloses a time synchronization model of an annular WSN pulse coupling oscillator based on a cellular automaton, belonging to the technical field of wireless network communication. The model is that each oscillator is regarded as a cell, and each oscillator in the oscillator system is represented by a grid in the cellular automaton; in the synchronous evolution process of the pulse coupled oscillator network, under the excitation coupling mechanism of 'one coupling and increasing', a plurality of oscillator groups appear in the system of nodes meeting the synchronous condition until only one oscillator group is finally realized gradually in a synchronous state; setting N oscillator nodes to form a nearest coupling network of a ring topology; mapping the stable state of the whole cellular automata system to the synchronization of the nearest neighbor network of the pulse coupled oscillator; in a wireless sensor network with a ring network topology, a nearest neighbor network synchronization model of a pulse coupled oscillator is constructed, and a time synchronization model of the nearest neighbor network of the WSN pulse coupled oscillator applied to the ring network topology is obtained.
Description
Technical Field
The invention particularly relates to a time synchronization model of an annular WSN pulse coupling oscillator based on a cellular automaton, and belongs to the technical field of wireless network communication.
Background
A Wireless Sensor Network (WSN) is a distributed system, and is one of the current research hotspots due to its wide application prospect. The wireless sensor network plays an important role in the fields of military monitoring, environmental monitoring, medical care, intelligent factories, intelligent cities, underground coal mine safety monitoring and the like. WSN nodes are independent of each other and communicate in a wireless mode, and each node maintains a local clock. The timing signal for the clock is typically provided by an inexpensive crystal oscillator. Due to the limitation of the manufacturing process of the crystal oscillator, and the influence of various accidental factors such as voltage, temperature, crystal aging and the like in the operation process, the frequency of the crystal oscillator is difficult to keep consistent, so that the timing rate of nodes in a network always has deviation, and the time of the nodes in the network is out of step. In order to maintain the consistency of the local time of the nodes, time synchronization operation must be performed frequently. Therefore, the requirement of the WSN for time synchronization is particularly important compared to a general distributed system, and it can be said that time synchronization is a supporting technology of the WSN. At present, almost all occasions such as positioning, ranging, data fusion, MAC layer protocols, sleep scheduling, routing protocols, cooperative transmission, database synchronization and the like have clear requirements on time synchronization.
Pulse coupled oscillators (Pulse coupled oscillators) transmit information to each other by means of signals in the form of pulses, such as firefly synchronous scintillations, cardiac pacemaker cells, etc., and network systems composed of such oscillators are called Pulse coupled systems (Pulse coupled systems). In the pulse coupling system of the full-connection network, all nodes transfer coupling information with each other, and although the coupling exists for a very short time, the whole system can show remarkable synchronism. The method is applied to WSN time synchronization, and can be used for synchronizing signals at a physical layer, and is independent of sources; the method can well adapt to the dynamic topology of the network and has good expandability; each node can achieve synchronization only by executing a same and simple mechanism, can not store time information, and is very suitable for wireless sensor networks with limited resources.
Although the pulse coupled oscillator network synchronization model is well applied to wireless sensor network time synchronization, it is limited to a fully connected network topology. For example, in the special physical environment of the underground coal mine, the underground physical environment of the coal mine is different from the ground, and the traditional two-dimensional network topology cannot be directly applied, for example, at a bifurcation of an underground tunnel, compared with a pulse coupled oscillator network synchronization model of a full-connection network, a complex underground tunnel is more suitable for a non-full-connection ring network topology. In the ring network topology, because the information transmission range of the pulse signal can only be in the nearest neighbor node, when a certain node cannot work normally, the ring network cannot realize synchronization. In the process of network synchronization, a large amount of pulse coupling information transfer is needed, and complete synchronization in a ring network is difficult to achieve.
Disclosure of Invention
The invention provides a time synchronization model of a wireless sensor network adaptive to a ring network topology, which is used for constructing a pulse coupled oscillator nearest neighbor network time synchronization model based on a cellular automaton by taking a non-leakage pulse coupled oscillator model as a theoretical model.
Specifically, the WSN pulse coupled oscillator time synchronization model based on the cellular automaton provided by the invention is as follows:
each oscillator is regarded as a cell, the oscillator is represented by a grid in a cellular automaton, and if some oscillator node in a pulse coupled oscillator network reaches an excited state to generate a pulse signal, other nodes are influenced by a coupling factor, so that the self phase is stimulated to change in state; in the process of synchronous evolution, under the excitation coupling mechanism, a plurality of oscillator groups appear in a system of nodes meeting the synchronous condition until a synchronous state is gradually realized when only one oscillator group exists finally;
setting N oscillator nodes to form a proximity coupling network, mapping the proximity coupling network into a one-dimensional cellular automaton in which N checks connected end to end are arranged in a line, regarding each oscillator as a cell, wherein one node in two states of the cell in an initial state of random distribution reaches an excited state, namely a '1' state; the non-excited state is a 0 state; with the interaction of a large number of cells through the synchronous evolution rule of the pulse coupled oscillator, all the grids are changed into excited states in the (N +1)/2 th row, and when the whole cellular automaton system reaches a stable state, the cells are mapped into the synchronization of the nearest neighbor network of the pulse coupled oscillator;
in a wireless sensor network with a ring network topology, a nearest neighbor network synchronization model of a pulse coupled oscillator is constructed, each oscillator is regarded as a sensor node, and the synchronization evolution of a synchronization system is mapped into the time synchronization of the wireless sensor network through the association mode of the oscillator, the cell, the oscillator and the sensor node, so that the nearest neighbor network time synchronization model of the WSN pulse coupled oscillator applied to the ring network topology is obtained.
The invention has the beneficial effects that:
the time synchronization of the needle ring chain-shaped wireless sensor network takes a pulse coupling network synchronization model as a theoretical basis, uses a linear state change function under a coupling and increasing mechanism of a firefly synchronization technology, combines a one-dimensional cellular automaton, and maps a synchronization form emerging from a 'rule 254' of the cellular automaton into the synchronization evolution of a nearest neighbor coupling network. A WSN pulse coupling oscillator nearest neighbor network time synchronization model based on a cellular automaton is provided through an oscillator-cellular-oscillator-sensor node association mode, and is suitable for a wireless sensor network time synchronization technology of a non-fully-connected ring network topology. Has certain theoretical guiding significance and application value for actual production.
Drawings
Fig. 1 is a schematic diagram of a nearest neighbor coupling network.
Fig. 2 is a diagram illustrating a linear variation function of a node of a pulse coupling network.
FIG. 3 is a schematic diagram of "rule 254".
FIG. 4 is a time-space diagram of cellular automata "rules 254".
Fig. 5 is a graph showing the phase change of 25 nodes with time.
FIG. 6 is a state response curve of the synchronization model.
Detailed Description
The following description of the embodiments of the present invention is provided with reference to the accompanying drawings:
aiming at the wireless sensor network with the ring network topology, the invention realizes the time synchronization of the wireless sensor network with the ring network topology by the information transmission mode that the one-dimensional cellular automata rule '254' model extends to the traditional pulse coupled oscillator network synchronization model, and constructs a WSN pulse coupled oscillator nearest neighbor network time synchronization model based on the cellular automata.
Each oscillator is regarded as a cell, the oscillator is represented by a grid in a cellular automaton, and if some oscillator node in a pulse coupled oscillator network reaches an excited state to generate a pulse signal, other nodes are influenced by a coupling factor, so that the self phase is stimulated to change in state. In the process of synchronous evolution, under the excitation coupling mechanism, a plurality of oscillator groups appear in a system of nodes meeting the synchronous condition until a synchronous state is gradually realized when only one oscillator group is finally arranged. Therefore, the one-dimensional cellular automaton is regularly set based on the above-mentioned "one-coupling-and-increasing" pulse coupled oscillator synchronization mechanism.
Setting N oscillator nodes to form a proximity coupling network, mapping the proximity coupling network into a one-dimensional cellular automaton in which N checks connected end to end are arranged in a line, regarding each oscillator as a cell, wherein one node in two states of the cell randomly distributed initial state reaches an excited state, namely a '1' state, and representing the node by a black check; the non-excited state is a "0" form, indicated by white squares. With the interaction of a large number of cells through the pulse coupled oscillator synchronous evolution rule, all the squares are changed into black in the (N +1)/2 th row, namely all the squares are in the form of '1', and when the whole cellular automata system reaches a stable state, the cells are mapped into the synchronization of the nearest neighbor network of the pulse coupled oscillator. This change is referred to as "rule 254" in the Wolfram's study of one-dimensional cellular automata.
In a wireless sensor network with a ring network topology, a nearest neighbor network synchronization model of a pulse coupled oscillator is constructed, each oscillator is regarded as a sensor node, and the synchronization evolution of a synchronization system is mapped into the time synchronization of the wireless sensor network through the association mode of the oscillator, the cell, the oscillator and the sensor node, so that the nearest neighbor network time synchronization model of the WSN pulse coupled oscillator applied to the ring network topology is obtained.
The following examples demonstrate the effectiveness of the present invention:
step 1: time synchronization model of nearest neighbor network of pulse coupled oscillator based on cellular automaton is constructed
(1) Coupling mechanism of nearest neighbor pulse coupling network of ring network topology
M&The S model is a pulse coupling model without coupling time lag, and is a network consisting of N nodes, each node is composed of a state variable xiIs expressed, and assume xiAccording to rule xi＝f(φi) From a lower threshold value xi0 continuously changes to reach the upper threshold xi1. And when xiWhen equal to 0, phiiWhen node i reaches the upper threshold x, 0iWhen 1, phi i1. Therefore, f satisfies f (0) 0 and f (1) 1. The model is to transmit the coupling stimulation information to each other through signals in the form of pulses, and in the pulse coupling network, although the coupling exists for a very short time, the coupling can emerge stronglySuch as the synchronous flickering phenomenon of fireflies.
In the pulse coupling network, the nearest neighbor coupling network is a non-fully-connected ring network topology, the networks are mutually coupled in a nearest neighbor mode, namely, the nodes are only coupled with the neighbor nodes adjacent to the nodes of the nodes, the system is a network consisting of pulse coupling oscillators with N being more than or equal to 3, all the nodes have the same dynamic behavior, and each node is composed of a state variable xiTo indicate. As shown in fig. 1, the coupling network is configured as a ring in a nearest neighbor node having N nodes, where each node is connected to only two neighbor nodes nearest to it. FIG. 2 is a schematic diagram showing a linear variation function of nodes of a pulse coupled network, each sensor node is regarded as a single pulse oscillator in a pulse coupled oscillator synchronization model applied to a wireless sensor network, and a pulse signal can be periodically output to act on other oscillators, and the model has a linear state function, wherein the linear variation function is shown as a formula (1)
x＝f(φ)＝φ,φ∈[0,1] (1)
When not coupled, the node implements periodic firing according to the following rules: when x isiReach the upper threshold value xiWhen 1, the node fires, while xiInstantaneously returning to the lower threshold value xiWhen the change rule is repeated, the next cycle starts, as in equation (2)
Wherein, i ═ {1, 2, 3 … … N };
when the whole network is coupled with each other by the pulse coupling mode of the nearest neighbor connection: when a given node fires at time t, it raises the state variables of its neighbors by epsilon units, or directly to the upper threshold 1, where epsilon is called the coupling strength of the network. Such as formula (3)
The system is in a random initial state if at t0Greater than or equal to 0, such that
At which point the network reaches a synchronized state.
Namely, the one-coupling-and-increasing mechanism of the pulse coupled oscillator network enables the state of each node to change, and in the complex synchronous evolution, the nodes in different states are coupled and changed, so that an oscillator group is formed among the nodes in the same state. When the whole pulse coupling network synchronously evolves to only two oscillator groups, then the oscillator group is formed, and the system gradually achieves synchronization.
(2) One-dimensional cellular automaton 'rule 254' model based on nearest neighbor coupling network
Cellular automata is a dynamic system defined in a cellular space composed of cells with discrete finite states and evolving in discrete time dimensions according to certain local rules. The components that make up cellular automata are called "cells", each cell having at a certain moment a state that selects only one of a certain finite set of states, the cells being regularly arranged on a spatial grid called "cell space", their respective states changing over time, being updated according to a local rule. The state of a cell at a certain time depends on the state of the cell at the previous time and the states of the left and right neighboring cells of the cell, the cells in the cell space are synchronously updated according to such local rules, and the whole cell space shows a change in a discrete time dimension.
The one-dimensional cellular automaton is basically composed of four parts, namely a cellular, a cellular space, a neighbor and a rule.
1) Cell: the cells are distributed on lattice points in a discrete one-dimensional space, and the state change is in a binary form of {0,1 }.
2) Cell space: theoretically, the euclidean space rule partition of any dimension is infinitely extended in each dimension. For a cellular automaton in one-dimensional space, the cellular space is represented as a "circle" that is connected end to end.
3) Neighbor: in one-dimensional cellular automata, the neighbors are usually determined by radius, and all cells within a cell are considered neighbors of the cell.
4) Rule: and determining the dynamic function of the cell state at the next moment according to the current state and the neighbor condition of the cell.
Let d represent the spatial dimension, k the state of a cell and take the value in a finite set S, and r the neighbor radius of a cell. Z is an integer set. t represents time, evolves in a discrete time dimension, and t +1 represents a state moment after the cell is subjected to regular evolution. When d is 1, the whole cellular space is in one-dimensional space, and the distribution of the state set S on the integer set Z is denoted as SZ. The dynamic evolution of cellular automata is the change of state combinations over time, which can be written as:
this dynamic evolution is in turn determined by local evolution rules f, also referred to as local rules, for the individual cells. For a one-dimensional space, a cell and its neighbors can be denoted as S2r+1The local function can then be written as:
for the local rule f, the input and output sets of the function are both finite sets, and when r is 1, the local change rule is independently applied to the cell i in the cell space to obtain the global evolution
Where there are three variables, each taking two state values, there are 2 x 2 ═ 8 combinations, and the values given on these 8 independent variable combinations determine f.
In the nearest neighbor coupled network, the state change mechanism of the pulse coupled oscillator network is as follows: the node and the adjacent neighbor nodes change the state through a mechanism of 'one coupling and one increasing' of the coupling strength; in the one-dimensional cellular automata, the change mechanism of a cellular automata system formed by a plurality of cells and connected in an end-to-end mode is as follows: the state of the self cell at the same moment is changed under the influence of the states of the neighbor cells at the next moment. The cellular automaton is composed of a large number of simple cells, central control is not available, each cell only interacts with a small number of other individuals, and for example, the firefly adjusts the self-flashing frequency according to the brightness and the extinguishment of surrounding fireflies. Therefore, each oscillator is regarded as a cell, and the synchronous emergence of the nearest neighbor coupling network is found in the one-dimensional cellular automaton.
In the one-dimensional cellular automaton based on the nearest neighbor coupling network, the state of a cell at the time t is the current state of a node of the pulse coupling network, and the state of the cell at the time t +1 is the node synchronization state emerging from a 'one coupling and increasing' mechanism in the pulse coupling network. Namely, in the changing process of the time from t to t +1, the occurrence of an oscillator synchronization group in the synchronization process of the adjacent pulse coupling network is included, namely, the adjacent nodes form an oscillator group after state synchronization and continue to participate in the synchronization evolution of the network. Therefore, the cells are connected end to end, each cell has two nearest neighbor cells, and if only one of the three cells has a cell shape of "1", the next time change of the middle cell is set to be "1". The mapping yields a formal rule for f:
[1,1,1]→1；[1,1,0]→1；[1,0,1]→1；[1,0,0]→1；
[0,1,1]→1；[0,1,0]→1；[0,0,1]→1；[0,0,0]→0；
the rule is represented graphically as follows (black squares for l, white squares for 0), and the change is referred to as "rule 254" in the Wolfram's study of cellular automata, as shown in figure 3.
Step 2: simulation of ring network topology synchronization process based on construction model
The cellular automaton is a dynamic system, and the state of a cell and its neighboring cells at time t +1 is determined by the state of the cell and its neighboring cells at time t. In the ring network topology, a WSN pulse coupled oscillator nearest neighbor network time synchronization model based on a cellular automaton is synchronously simulated.
First, the system is initially assigned at time t, assuming that the first row of cell spaces end-to-end has only one excited state, namely "1" (represented by black squares). Then, the state of the middle cell at the next moment is obtained by updating the states of the three cells, and the state result of each row of cells is observed. And finally, researching the overall behavior of the system based on local interaction, programming and operating a cellular automaton through Mathemica software, and drawing to obtain a space-time diagram. Fig. 4 shows a space-time diagram of the cellular automata, which shows that the cellular automata changes with time, the top row is the initial state setting of the one-dimensional cellular automata, and the updated state of each step is arranged below the top row. In the case of only one excited cell in the initial state in the space-time diagram, the states of all cells tend to be the same under the action of time change and a 'one-coupling-and-one-increasing' change mechanism.
And step 3: synchronization process tracking for WSN time synchronization of ring network topology based on construction model
(1) Phase tracking of nodes in a system
In a WSN nearest neighbor pulse coupled oscillator time synchronization model of a ring network topology, phase changes of oscillator nodes are tracked, and therefore the synchronization process of the model is observed. First, different initial phases are set for all oscillator nodes in the system, so that the system is initially in an out-of-sync state. Then, the process of synchronizing the whole system at equal intervals is phase sampling, and phase information of all nodes in the system at a certain moment is obtained. And finally, observing the synchronization process of the whole ring network by analyzing the phase change of each node sampled at each equal interval. As shown in fig. 5, it is a phase change situation of a ring network composed of 25 nodes with time of phase in a nearest neighbor coupled pulse coupled oscillator synchronization model, a neighbor oscillator node adjusts its own phase according to the coupling strength of an excited oscillator, and finally all excited oscillators are combined into an oscillator group, and each node gradually achieves phase synchronization from different phases of an initial state.
(2) Verifying synchronization effect of constructed model
In the WSN nearest neighbor pulse coupled oscillator time synchronization model of the ring network topology, the respective linear change functions of different nodes can reflect the state change process of the nodes in each synchronization process of the synchronization period. Due to the excitation effect of the coupling strength, the node has a state improving effect, and therefore the synchronization effect of the synchronization model is verified through the state response curve. As shown in fig. 6, in the process of a synchronization simulation experiment, state analysis is performed on nodes with different initial states in a network, a state response curve of the node is obtained along with the increase of the number of synchronization times, and it is observed that each node is promoted under the influence of excitation of the coupling strength of a neighboring excitation node, and finally, a linear change function can be used to represent the state change of all the nodes, so that the nodes with different states gradually tend to a synchronization state.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (1)
1. A time synchronization model of an annular WSN pulse coupling oscillator based on a cellular automaton is characterized in that the model is as follows:
each oscillator is regarded as a cell, the oscillator is represented by a grid in a cellular automaton, and if some oscillator node in a pulse coupled oscillator network reaches an excited state to generate a pulse signal, other nodes are influenced by a coupling factor, so that the self phase is stimulated to change in state; in the process of synchronous evolution, under the excitation coupling mechanism, a plurality of oscillator groups appear in a system of nodes meeting the synchronous condition until a synchronous state is gradually realized when only one oscillator group exists finally;
setting N oscillator nodes to form a proximity coupling network, mapping the proximity coupling network into a one-dimensional cellular automaton in which N checks connected end to end are arranged in a line, wherein one node in two states of the cellular automaton is randomly distributed to an initial state and reaches an excited state, namely a '1' state; the non-excited state is a 0 state; with the interaction of a large number of cells through the synchronous evolution rule of the pulse coupled oscillator, all the grids are changed into excited states in the (N +1)/2 th row, and when the whole cellular automaton system reaches a stable state, the cells are mapped into the synchronization of the nearest neighbor network of the pulse coupled oscillator;
in a wireless sensor network with a ring network topology, constructing a nearest neighbor network synchronization model of a pulse coupled oscillator, regarding each oscillator as a sensor node, and mapping the synchronization evolution of a synchronization system into the time synchronization of the wireless sensor network through the association mode of the oscillator, the cell, the oscillator and the sensor node to obtain the nearest neighbor network time synchronization model of the WSN pulse coupled oscillator applied to the ring network topology;
the coupling mechanism of the nearest neighbor pulse coupling network of the ring network topology in the model is specifically as follows:
M&the S model is a pulse coupling model without coupling time lag, and is a network consisting of N nodes, each node is composed of a state variable xiIs expressed, and assume xiAccording to rule xi＝f(φi) From a lower threshold value xiContinuously varying at 0 to reach the upper threshold xi1 is ═ 1; and when xiWhen equal to 0, phiiWhen node i reaches the upper threshold x, 0iWhen 1, phii1 is ═ 1; thus, f satisfies f (0) 0, f (1) 1;
in the pulse coupling network, the nearest neighbor coupling network is a non-fully connected ring network topology, the networks are mutually coupled in a nearest neighbor mode, namely, the node only performs coupling action with the adjacent neighbor nodes of the node,the system is a network consisting of pulse coupled oscillators with N being more than or equal to 3, all nodes have the same dynamic behavior, and each node is provided with a state variable xiTo represent; a nearest neighbor node coupling network with N nodes is set to be a ring type, wherein each node is only connected with two nearest neighbor nodes; in a pulse coupled oscillator synchronization model applied to a wireless sensor network, each sensor node is regarded as a single pulse oscillator, and a pulse signal can be periodically output to act on other oscillators, wherein the model has a linear state function, and the linear change function is shown as a formula I
x (phi) is f (phi), phi belongs to [0,1] formula one
When not coupled, the node implements periodic firing according to the following rules: when x isiReach the upper threshold value xiWhen 1, the node fires, while xiInstantaneously returning to the lower threshold value xiRepeat the change rule and start the next cycle, as equation two
Wherein, i ═ {1, 2, 3 … … N };
when the whole network is coupled with each other by the pulse coupling mode of the nearest neighbor connection: when a given node fires at time t, it raises the state variable of its neighbor nodes by epsilon units, or directly to the upper threshold 1, where epsilon is called the coupling strength of the network; such as formula three
The system is in a random initial state if at t0Greater than or equal to 0, such that
At this point the network reaches a synchronized state;
namely, a 'one-coupling-and-increasing' mechanism of a pulse coupled oscillator network enables the state of each node to change, and in complex synchronous evolution, the nodes in different states are coupled and changed to form an oscillator group among the nodes in the same state; when the whole pulse coupling network synchronously evolves to only two oscillator groups, the oscillator group is formed, and the system gradually achieves synchronization;
the one-dimensional cellular automata rule 254 model based on the nearest neighbor coupling network in the model specifically comprises:
the cellular automaton is a dynamic system defined in a cellular space consisting of cells with discrete and finite states and evoluted in a discrete time dimension according to a certain local rule; the components that make up cellular automata are called cells, each cell having at a certain moment a state that is chosen to be only one of a finite set of states, these cells being regularly arranged on a spatial grid called "cell space", their respective states changing over time, being updated according to a local rule; the state of a cell at a certain moment depends on the state of the cell at the last moment and the states of the left and right neighbor cells of the cell, the cells in the cell space are synchronously updated according to the local rule, and the whole cell space shows the change in discrete time dimension;
the one-dimensional cellular automaton is basically composed of four parts, namely a cellular, a cellular space, a neighbor and a rule;
cell: the cells are distributed on lattice points in a discrete one-dimensional space, and the state change of the cells is a binary form of {0,1 };
cell space: theoretically, the method is divided by Euclidean space rules of any dimension, and each dimension is extended infinitely; for a cellular automaton in a one-dimensional space, the cellular space is represented as a 'circle' connected end to end;
neighbor: in one-dimensional cellular automata, the neighbors are usually determined by the radius, and all cells within a cell are considered as neighbors of the cell;
rule: determining a dynamic function of the cell state at the next moment according to the current state and the neighbor state of the cell;
setting d to represent space dimension, k to represent the state of a cell and taking a value in a finite set S, and r to represent the neighbor radius of the cell; z is an integer set; t represents time, evolves on a discrete time dimension, and t +1 represents state time of the cell after being subjected to regular evolution; when d is 1, the whole cellular space is in one-dimensional space, and the distribution of the state set S on the integer set Z is denoted as SZ(ii) a The dynamic evolution of cellular automata is the change of state combinations over time, which can be written as:
the dynamic evolution is determined by local evolution rules f of each cell, and the local function f is also called local rule; for a one-dimensional space, a cell and its neighbors can be denoted as S2r+1The local function can then be written as:
for the local rule f, the input and output sets of the function are both finite sets, and when r is 1, the local change rule is independently applied to the cell i in the cell space to obtain the global evolution
Three variables, each of which takes two state values, there are 2 × 2 × 2 ═ 8 combinations, and values given over these 8 independent variable combinations are used to determine f;
in the nearest neighbor coupled network, the state change mechanism of the pulse coupled oscillator network is as follows: the node and the adjacent neighbor nodes change the state through a mechanism of 'one coupling and one increasing' of the coupling strength; in the one-dimensional cellular automata, the change mechanism of a cellular automata system formed by a plurality of cells in an end-to-end connection mode is as follows: the state of the self cell at the same moment is changed under the influence of the states of the neighbor cells at the next moment; the cellular automaton is composed of a large number of simple cells, central control does not exist, and each cell only interacts with a small number of other individuals; therefore, the synchronous emergence of the nearest neighbor coupling network is found in the one-dimensional cellular automaton;
in the one-dimensional cellular automaton based on the nearest neighbor coupling network, the state of a cell at the time t is the current state of a pulse coupling network node, and the state of the cell at the time t +1 is the node synchronization state emerging from a 'one coupling and increasing' mechanism in the pulse coupling network; namely, in the change process from t to t +1, the occurrence of an oscillator synchronization group in the synchronization process of the adjacent pulse coupling network is included, namely, the adjacent nodes form an oscillator group after state synchronization and continue to participate in the synchronization evolution of the network; therefore, the cells are connected in an end-to-end manner, each cell has two nearest neighbor cells, and as long as one cell form of '1' is contained in the three cells, the change of the middle cell at the next moment is set to be '1'; the mapping results in a formal rule for f.
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