CN106877997A - A kind of three-dimensional chaotic system that may result from sharp or hiding attractor - Google Patents
A kind of three-dimensional chaotic system that may result from sharp or hiding attractor Download PDFInfo
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- CN106877997A CN106877997A CN201710231004.4A CN201710231004A CN106877997A CN 106877997 A CN106877997 A CN 106877997A CN 201710231004 A CN201710231004 A CN 201710231004A CN 106877997 A CN106877997 A CN 106877997A
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Abstract
The invention discloses it is a kind of it is special, while have the three-dimensional chaotic system of conservative and dissipativeness, with the change of control parameter, system balancing point coexists behavior without being changed between equalization point and 2 non-zero equalization points, form self-excitation or hiding multi attractor.Using commercial discrete component, the corresponding hardware circuit of the system is devised, the circuit system is easy to numerical value, circuit simulation and experimental observation, and larger progradation is played in the application of engineering field for chaos system.
Description
Technical field
The present invention realize it is a kind of produce hide or self-oscillation attractor special chaos signal source.
Background technology
Chaos as a kind of distinctive kinematics behavior in Kind of Nonlinear Dynamical System, with the sensitivity extreme to initial value
Property and intrinsic stochasticity, make it cause scholar greatly to pay close attention in the science such as electronics, communication, information processing or engineering field；20
The sixties in century, Lorenz was when air motion is studied, and when the atmosphere data that will be gathered is processed, was found surprisingly that data limited
With time unlimited not circulation change in spatial dimension, that is, strange attractor is occurred in that, afterwardsO E are proposedIt is mixed
Ignorant system, the system is than Lorenz simple system and possesses topological structure different from Lorenz systems.Hereafter academia for
The research of the chaos system that ODE is constituted never rested with excavation, and Chen Guanrong proposes Chen systems, subsequent Lv Jin
Tiger then has also been proposed L ü chaos systems.Hereafter, new chaos system is constantly produced, there is Liu chaos systems, hyperchaos L ü systems
System, Bao chaos systems etc..
Further investigation with people to chaos system, fundamental characteristics and dynamic behavior to chaos understand further, mix
Ignorant system is more deep in the application of science, engineering field, because chaos is to primary condition and parameter extreme sensitivity, with fabulous
Randomness；It is more just that chaos signal generator is built currently with discrete components such as operational amplifier, resistance and electric capacity
The mode of profit, it is possible to achieve purposefully control chaotic, also enables chaos be applied in more fields.
Class phenomenon --- the multistability for newly defining in recent years, i.e., in the case where circuit parameter is constant, original state
Difference, system operation track may be stable at the different state such as an attractor, chaos, paracycle, cycle, and this phenomenon is claimed
It is multistability；To there is many stabilizations or the chaos system of super multistability to be applied in chaotic secret communication, Ke Yiyou
Improve the security performance of system in effect ground.Therefore, the multistability of research chaos system has important theory and realistic meaning.
The content of the invention
The technical problems to be solved by the invention are a kind of three-dimensional chaos systems that may result from sharp or hiding attractor of design
System, realizes to its hardware circuit.
In order to solve the above technical problems, the invention provides a kind of three-dimensional chaos system that may result from sharp or hiding attractor
System, devises corresponding hardware circuit, and its structure is as follows：
The main circuit includes：Integrating channel one, integrating channel two and integrating channel three；Integrating channel one has 5 inputs
End, respectively 1 "-vy", 2 "-vx", 1 " vy" and 1 " vz", by exporting " v after multiplier and integratorx", then pass through
One-level phase inverter final output "-vx”；Integrating channel two has 4 inputs, respectively "-V1”、“vx”、“–vy" and " vz", pass through
" v is exported after multiplier and integratory", then by one-level phase inverter final output "-vy”；Integrating channel three have 3 inputs "-
vx”、“vx" and " vy", by exporting " v after multiplier and integratorz”；Operational amplifier U1、U2、U3、U4And U5Homophase input
Termination " ", "-V1" end offer " -1V " DC voltage.
In integrating channel one, input "-vy" series connection one " 20k Ω " resistance be connected to operational amplifier U1It is anti-phase defeated
Enter end；Input "-vx" and " vy" through multiplier M1Series resistance R after multiplicationaIt is connected to operational amplifier U1Inverting input；It is defeated
Enter end "-vx" and " vz" through multiplier M2The resistance of series connection one " 20k Ω " is connected to operational amplifier U after multiplication1Anti-phase input
End；U1Inverting input and output end between shunt capacitance C1, now U1Output end output " vx”；U1Output end and computing
Amplifier U2Inverting input between connect the resistance of " 10k Ω "；U2Inverting input and output end between in parallel one
The resistance of individual " 10k Ω ", now U2Output end output "-vx”；Operational amplifier U1And U2In-phase input end connect " ".
In integrating channel two, input "-V1" series resistance RbIt is connected to operational amplifier U3Inverting input；Input
“vx" through multiplier M3Series resistance R after square operation is made in multiplicationcIt is connected to operational amplifier U3Inverting input；Input "-
vy" and " vz" through multiplier M4The resistance of series connection one " 20k Ω " is connected to operational amplifier U after multiplication3Inverting input；U3's
Shunt capacitance C between inverting input and output end2, now U3Output end output " vy”；U3Output end and operational amplifier
U4Inverting input between connect the resistance of " 10k Ω "；U4Inverting input and output end between one " 10k of parallel connection
The resistance of Ω ", now U4Output end output "-vy”；Operational amplifier U3And U4In-phase input end connect " ".
In integrating channel three, input "-vx" series connection one " 20k Ω " resistance be connected to operational amplifier U5It is anti-phase defeated
Enter end；Input " vx" through multiplier M5The resistance that series connection one " 20k Ω " after square operation is made in multiplication is connected to operational amplifier U5
Inverting input；Input " vy" through multiplier M6The resistance that series connection one " 20k Ω " after square operation is made in multiplication is connected to computing
Amplifier U5Inverting input；U5Inverting input and output end between shunt capacitance C3, now U5Output end output
“vz”；Operational amplifier U5Homophase input termination " ".
It is described it is a kind of may result from swashing or hiding attractor the corresponding main circuit of three-dimensional chaotic system as shown in figure 1,
System equation contains three state variables x, y and z；Corresponding circuits state equation contains three state variable vx、vyAnd vz。
Beneficial effects of the present invention are as follows：A kind of three-dimensional chaotic system that may result from sharp or hiding attractor is proposed, if
Its hardware circuit is counted, a kind of hiding or self-oscillatory chaos signal source is realized.The system architecture is simple, it is easy to theory point
Analysis and circuit are integrated, there is larger engineering application value.
Brief description of the drawings
In order that present disclosure is more likely to be clearly understood, below according to specific embodiment and with reference to accompanying drawing,
The present invention is further detailed explanation：
A kind of three-dimensional chaotic system hardware circuit implementations that may result from sharp or hiding attractor of Fig. 1；
Fig. 2 chooses primary condition (0,0,0) in vx-vyThe numerical simulation phase rail figure and experiment results of plane；
Fig. 3 chooses primary condition (1,0,1) in vx-vyThe numerical simulation phase rail figure and experiment results of plane；
Fig. 4 chooses primary condition (2,0,0) in vx-vyThe numerical simulation phase rail figure and experiment results of plane；
Specific embodiment
Mathematical modeling：A kind of three-dimensional autonomy oscillating circuit that may result from sharp or hiding attractor of the present embodiment builds such as
Shown in Fig. 1.First, the present invention is based on a three-dimensional chaotic system, and system can be described by following dimensionless state equation：
Wherein, x, y, z is 3 state variables, and a, b, c are 3 new control parameters for introducing and are normal number.
Make the equation left side of system (1) be equal to zero, have
Can be changed into by computing
x[(c-a)x2+ (a-1) x+1-b]=0 (3)
Can verify, x=0 is not the solution of formula (2), i.e., system (1) is without non-zero equalization point.As fixed c=2, that
By the solution of following 5 kinds of situation discussions (2), and determine the equalization point of system (1).
Situation one：A=2, b=1.Without solution, i.e., system (1) is without equalization point for formula (2).
Situation two：A=2,1<b<2.Formula (2) has 2 solutions, and the 2 non-zero equalization points that thus can parse the system of obtaining (1) are
Situation three：A=2, b≤1 or b >=2., without solution, system (1) is without equalization point for formula (2).
Situation four：1<a<1.5th, b=1.Formula (2) has 2 solutions, and the 2 non-zero equalization points that can parse the system of obtaining (1) are
Situation five：A≤1 or a >=1.5, b=1., without solution, system (1) is without equalization point for formula (2).
In sum, it is possible to find exist without being cut between equalization point and 2 non-zero equalization points when system (1) is with Parameters variation
Change, i.e., the system may result from swashing or hiding attractor.
Numerical simulation：Using MATLAB simulation Software Platforms, numerical simulation can be carried out to the system as described by formula (4)
Analysis.Selection Runge-Kutta (ODE23) algorithm is solved to system equation, can obtain the phase rail figure of this state of chaotic system variable.
Canonical parameter a=2, b=1, c=2 are chosen, the MATLAB numerical simulation phase rails figure under the different initial values of correspondence is respectively such as Fig. 2
Shown in (a), Fig. 3 (a) and Fig. 4 (a).
Experimental verification：The design uses the operational amplifier of model AD711KN, and provides ± 15V operating voltages.Its
In, vx、vy、vz3 capacitance voltage state variables, C=C are represented respectively1=C2=C3=0.1 μ F, Ra=10k Ω, Rb=20k Ω
And Rc=10k Ω.Using accurate adjustable resistance, electric capacity is ROHS to resistance.Theory analysis and numerical simulation show, the electricity
Chaos attractor produced by road is more sensitive to original state, constantly opens and closes power supply, it is easy to needed for realizing
The state variable initial value wanted.Measured waveform is captured using Tektronix DPO3034 digital storage oscilloscopes, logarithm value is imitated respectively
Chaos attractor phase rail figure in very has carried out experimental verification, and experimental result is respectively such as such as Fig. 2 (b), Fig. 3 (b) and Fig. 4 (b) institutes
Show.
Comparing result can be illustrated：The non-linear phenomena observed in experimental circuit fits like a glove with simulation result, can be with
Proof theory analyzes the correctness with numerical simulation.Therefore, the one kind constructed by the present invention may result from swashing or hiding attractor
Three-dimensional autonomous system hardware circuit there is the theoretical foundation and realizability physically of science, can be to chaos system circuit
Engineer applied plays positive impetus.
Above-described embodiment is only intended to clearly illustrate example of the present invention, and is not to embodiment party of the invention
The restriction of formula.For those of ordinary skill in the field, it is different that other can also be made on the basis of the above description
The change or variation of form.There is no need and unable to be exhaustive to all of implementation method.
Claims (3)
1. it is a kind of may result from swashing or hiding attractor three-dimensional chaotic system, it is characterised in that：Circuit includes that three integrations are logical
Road, with the change of circuit parameter, the circuit system equalization point is formed without being changed between equalization point and 2 non-zero equalization points
Self-excitation or hiding multi attractor coexist behavior.
2. it is according to claim 1 it is a kind of may result from swashing or hiding attractor three-dimensional chaotic system, it is characterised in that：
The three-dimensional chaotic system includes integrating channel one, integrating channel two and integrating channel three；Integrating channel one has 5 inputs,
Respectively 1 "-vy", 2 "-vx", 1 " vy" and 1 " vz", by exporting " v after multiplier and integratorx", then by one
Level phase inverter final output "-vx”；Integrating channel two has 4 inputs, respectively "-V1”、“vx”、“–vy" and " vz", by multiplying
" v is exported after musical instruments used in a Buddhist or Taoist mass and integratory", then by one-level phase inverter final output "-vy”；Integrating channel three have 3 inputs "-
vx”、“vx" and " vy", by exporting " v after multiplier and integratorz”；Operational amplifier U1、U2、U3、U4And U5Homophase input
Termination " ", "-V1" end offer " -1V " DC voltage.
3. it is according to claim 1 and 2 it is a kind of may result from swashing or hiding attractor three-dimensional chaotic system, its feature exists
In system equation contains three state variables x, y and z；Corresponding circuits state equation contains three state variable vx、vyAnd vz。
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107819566A (en) * | 2017-11-15 | 2018-03-20 | 杭州电子科技大学 | A kind of implementation method of new chaotic oscillating circuit |
| CN109033602A (en) * | 2018-07-18 | 2018-12-18 | 郑州轻工业学院 | One kind four times three-dimensional memristor circuit systems and realization circuit |
| CN111211885A (en) * | 2019-12-19 | 2020-05-29 | 哈尔滨工程大学 | Multi-stability chaotic system with impulse function form Lyapunov exponent |
| CN111538245A (en) * | 2020-06-26 | 2020-08-14 | 西京学院 | Robust control method of chaotic system with hidden attractor |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2013103971A1 (en) * | 2012-01-06 | 2013-07-11 | University Of New Hampshire | Systems and methods for chaotic entanglement using cupolets |
| CN104486064A (en) * | 2015-01-08 | 2015-04-01 | 常州大学 | Memory resistance chaotic signal producing circuit with self-excitation attractor and hidden attractor |
| CN105187191A (en) * | 2015-09-01 | 2015-12-23 | 王晓红 | Right-deviation three-dimensional single-scroll chaotic system and circuit |
| CN105227290A (en) * | 2015-09-01 | 2016-01-06 | 高建红 | A kind of three-dimensional four wing continuous chaotic system of singly balanced point and circuit |
| CN105406959A (en) * | 2015-11-08 | 2016-03-16 | 常州大学 | Improved Chua's system of three-scroll attractor capable of generating one self-excited scroll and two hidden scrolls simultaneously |
| CN105681020A (en) * | 2016-03-12 | 2016-06-15 | 常州大学 | Hyperchaotic hidden oscillation circuit based on balance-point-free memristor system |
| CN106506139A (en) * | 2017-01-12 | 2017-03-15 | 西京学院 | A kind of hiding attractor chaos circuit with stable equilibrium point |
-
2017
- 2017-04-11 CN CN201710231004.4A patent/CN106877997A/en active Pending
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2013103971A1 (en) * | 2012-01-06 | 2013-07-11 | University Of New Hampshire | Systems and methods for chaotic entanglement using cupolets |
| CN104486064A (en) * | 2015-01-08 | 2015-04-01 | 常州大学 | Memory resistance chaotic signal producing circuit with self-excitation attractor and hidden attractor |
| CN105187191A (en) * | 2015-09-01 | 2015-12-23 | 王晓红 | Right-deviation three-dimensional single-scroll chaotic system and circuit |
| CN105227290A (en) * | 2015-09-01 | 2016-01-06 | 高建红 | A kind of three-dimensional four wing continuous chaotic system of singly balanced point and circuit |
| CN105406959A (en) * | 2015-11-08 | 2016-03-16 | 常州大学 | Improved Chua's system of three-scroll attractor capable of generating one self-excited scroll and two hidden scrolls simultaneously |
| CN105681020A (en) * | 2016-03-12 | 2016-06-15 | 常州大学 | Hyperchaotic hidden oscillation circuit based on balance-point-free memristor system |
| CN106506139A (en) * | 2017-01-12 | 2017-03-15 | 西京学院 | A kind of hiding attractor chaos circuit with stable equilibrium point |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107819566A (en) * | 2017-11-15 | 2018-03-20 | 杭州电子科技大学 | A kind of implementation method of new chaotic oscillating circuit |
| CN107819566B (en) * | 2017-11-15 | 2020-06-19 | 杭州电子科技大学 | Method for realizing chaotic oscillating circuit |
| CN109033602A (en) * | 2018-07-18 | 2018-12-18 | 郑州轻工业学院 | One kind four times three-dimensional memristor circuit systems and realization circuit |
| CN109033602B (en) * | 2018-07-18 | 2020-05-22 | 郑州轻工业学院 | Quartic three-dimensional memristor circuit system and implementation circuit |
| CN111211885A (en) * | 2019-12-19 | 2020-05-29 | 哈尔滨工程大学 | Multi-stability chaotic system with impulse function form Lyapunov exponent |
| CN111538245A (en) * | 2020-06-26 | 2020-08-14 | 西京学院 | Robust control method of chaotic system with hidden attractor |
| CN111538245B (en) * | 2020-06-26 | 2022-06-03 | 西京学院 | Robust control method of chaotic system with hidden attractor |
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