CN109714147A - A kind of building and its circuit realization of the dissipation hyperchaotic system of double-wing chaotic attractor - Google Patents
A kind of building and its circuit realization of the dissipation hyperchaotic system of double-wing chaotic attractor Download PDFInfo
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Abstract
The present invention relates to a kind of buildings of the dissipation hyperchaotic system of double-wing chaotic attractor and its circuit to realize.Compared with dissipation chaos system, the safety of chaotic secret communication and Information Encryption Based on Chaotic Sequences can be improved in complicated dissipation hyperchaos signal, general deciphering method such as phase space reconfiguration, Hui-Hui calendar and nonlinear prediction etc. are difficult to decode the useful information for using hyperchaos signal encryption, therefore are an important topic of chaos applications in information engineering field to the research of dissipation hyperchaos.The present invention constructs the dissipation hyperchaotic system and its circuit of a kind of double-wing chaotic attractor, provides a kind of new method and thinking for the application of chaos system.FPGA of the invention realizes that circuit is made of dissipation hyperchaotic system module, key module, data output selecting module, D/A converter module and AD9767.
Description
Technical field
The present invention relates to a kind of chaos system and its circuit, in particular to the dissipation hyperchaotic system of a kind of double-wing chaotic attractor
Building and its circuit realize.
Background technique
Compared with chaos system, hyperchaotic system has two or more positive Lyapunov indexes, and phase rail is more
Multi-direction upper separation, dynamic behavior are increasingly complex.Chaotic secret communication and chaos can be improved in complicated hyperchaos signal
The safety of information encryption, general deciphering method such as phase space reconfiguration, Hui-Hui calendar and nonlinear prediction etc., which are difficult to decode, to be adopted
It will be one of chaos applications in information engineering field with the useful information of hyperchaos signal encryption, therefore to the research of hyperchaos
Important topic.The invention proposes a kind of buildings of the dissipation hyperchaotic system of double-wing chaotic attractor and its circuit to realize, is chaos
Systematic difference provides a kind of new method and thinking.
Summary of the invention
The purpose of the present invention is construct the dissipation hyperchaotic system and its circuit of a kind of double-wing chaotic attractor.With dissipation chaos system
System is compared, and the dynamic behavior of the dissipation hyperchaotic system is increasingly complex, has important research significance.
The technical solution adopted by the present invention to solve the above technical problem is:
1. a kind of construction method of the dissipation hyperchaotic system of double-wing chaotic attractor, which is characterized in that a kind of double-wing chaotic attractor
Dissipation hyperchaotic system mathematical model are as follows:
Wherein x, y, z, w are variable, and a, b, c are real number.
Work as a=5, when b=10, c=3, the equation of system (1) becomes:
Taking initial value is [1,1,1,1], and system has double-wing chaotic attractor, and 4 Lyapunov indexes are respectively L1=
0.2625、L2=0.0632, L3=0.0034 and L4=-12.8214, the Lyapunov dimension of system are DL=2.0257.Thus
As it can be seen that system tool is dimension there are two positive Lyapunov index and Lyapunov dimension, so that verifying system is a consumption
Dissipate hyperchaotic system.
2. a kind of Multisim artificial circuit of the dissipation hyperchaotic system of double-wing chaotic attractor is realized, which is characterized in that adopt
With linear resistance, capacitor, LM2924N type operational amplifier and MULTIPLIER analog multiplier, to have devised a mould
Quasi- electronic circuit.According to Analogical Electronics figure and Circuit theory, circuit equation is obtained are as follows:
3. a kind of FPGA circuitry of the dissipation hyperchaotic system of double-wing chaotic attractor is realized, which is characterized in that formula (1) is used Europe
Formula discretization is drawn, the discretization equation of dissipation hyperchaotic system is obtained are as follows:
Wherein, h is discrete sampling time step.
Detailed description of the invention
To make the object, technical solutions and advantages of the present invention clearer, the present invention is made into one below in conjunction with attached drawing
The detailed description of step:
Fig. 1 is x-y, x-z, y-z, z-w phasor of MATLAB of the present invention emulation；
Lyapunov exponential spectrum when Fig. 2 is [0,12] b ∈ of the present invention；
Bifurcation graphs when Fig. 3 is [0,12] b ∈ of the present invention；
Fig. 4 is power spectrum of the invention；
Fig. 5 is Poincar é sectional view of the invention；
Fig. 6 is Multisim artificial circuit figure of the invention；
Fig. 7 is x-y, x-z, y-z, z-w phasor of Multisim of the present invention emulation；
Fig. 8 is that FPGA of the invention realizes system block diagram.
Specific embodiment
Hereinafter reference will be made to the drawings, and the present invention is described in detail.
Specific embodiment 1: present embodiment is directed to a kind of dissipation hyperchaos system of double-wing chaotic attractor proposed by the present invention
The building of system is described in detail:
1. a kind of construction method of the dissipation hyperchaotic system of double-wing chaotic attractor, which comprises the following steps:
A kind of mathematical model of the dissipation hyperchaotic system of double-wing chaotic attractor are as follows:
Wherein x, y, z, w are variable, and a, b, c are real number.
Work as a=5, when b=10, c=3, the equation of system (1) becomes:
Taking initial value is [1,1,1,1], and there are a typical double-wing chaotic attractors for system, as shown in Figure 1.
2. the kinetic characteristics of dissipation hyperchaotic system
(1) equalization point and stability
The equalization point of system (1) can solve following Algebraic Equation set and obtain:
3 equalization points can be obtained in solution formula (3), are respectively as follows:
S0=(0,0,0)；
System is in equalization point (x*,y*,z*) at Jacobi matrix are as follows:
Det (λ I-J)=0 is enabled, obtaining its proper polynomial is f (λ)=λ4+A3λ3+A2λ2+A1λ+A0, wherein
A3=a-b+c-z*；
A2=x*2-y*2+z*2+1-ab+ac-bc+bz*-cz*-x*y*；
A1=a+c-2z*+ax*2+by*2+cz*2+bcz*+bx*y*+2x*y*z*-abc；
A0=ac-2cz*-2x*y*-x*2-y*2。
Work as a=5, when b=10, c=3, the stability of equalization point is as shown in table 1.
The stability of 1 equalization point of table
(2) Lyapunov index, Lyapunov dimension and bifurcation graphs
Lyapunov index (being abbreviated as LE) is that quantitative description state space chaos attractor path is each other in chaos system
The amount repelled and attracted.The sum of Lyapunov index is commonly used to the conservative and dissipativeness of judgement system, if Lyapunov index
The sum of (L=L1+L2+L3+L4) it is zero, then otherwise it is dissipative system that chaos system, which is Conservative Systems,.
Lyapunov dimension is
Work as a=5, c=3, when initial value is [1,1,1,1], the program worked out using Jacobi matrix method is utilized
The Lyapunov exponential spectrum that system (1) has been calculated in MATLAB software is as shown in Figure 2.Point that system variable z changes with parameter b
Trouble figure is as shown in Figure 3.When taking b=10,4 Lyapunov indexes of system are respectively L1=0.2625, L2=0.0632, L3=
0.0034 and L4=-12.8214, then Lyapunov dimension is DL=2.0257.In conjunction with Fig. 2 and Fig. 3 it is found that system at least has
Two positive Lyapunov indexes and Lyapunov dimension are dimension, so that verifying system is a dissipation hyperchaotic system.
(3) power spectrum and Poincar é sectional view
Numerical solution is carried out to formula (1) using quadravalence Runge-Kutta (ODE45) algorithm, system power spectrum can be obtained such as Fig. 4 institute
Show.The section Poincar é of selection further illustrates system complex as shown in figure 5, therefrom see some sheet of points off density
Chaotic behavior.
Specific embodiment 2: present embodiment is directed to a kind of dissipation hyperchaos system of double-wing chaotic attractor proposed by the present invention
The Multisim artificial circuit realization of system is described in detail:
1. using linear resistance, capacitor, LM2924N type operational amplifier and MULTIPLIER analog multiplier, to set
It is as shown in Figure 6 an Analogical Electronics has been counted out.
2. obtaining circuit equation according to Fig. 6 and Circuit theory are as follows:
3. R in formula (5)1~R24For resistance, C1~C4For capacitor.Take C1=C2=C3=1 μ F, R5=R11=R15=R21=
100kΩ.Enable R2=R3=R4=R6=R7=R8=R9=R10=R16=R17=R20=R22=R23=1k Ω passes through comparison system
Coefficient in system (1), can be calculated R1=2k Ω, R12=R18=R19=R24=10k Ω, R13=R14=3k Ω.Fig. 7 is oscillography
The result observed on device, it can be seen that experimental result is consistent with Numerical Simulation Results.
Specific embodiment 3: present embodiment is directed to a kind of dissipation hyperchaos system of double-wing chaotic attractor proposed by the present invention
The FPGA circuitry realization of system is described in detail:
1. formula (1) is used Euler's formula discretization, the discretization equation of dissipation hyperchaotic system is obtained are as follows:
Wherein, h is discrete sampling time step.
2. the system block diagram that the FPGA of dissipation hyperchaotic system is realized is as shown in Figure 8.The system block diagram is by dissipation hyperchaos
System module, key module, data output selecting module, D/A converter module and AD9767 composition.Dissipation hyperchaotic system mould
Block realizes chaos system；Key module generates control signal, exports selecting module for data；Data export selecting module from consumption
Dissipate selection two paths of signals output in four road signals of hyperchaotic system module output；D/A converter module is used to turn output signal
Being changed to AD9767 being capable of received signal；AD9767 is used to convert mould for the two-way output that dissipation hyperchaotic system module exports
Quasi- signal is so as to oscillograph observation.
3. the output of dissipation hyperchaotic system is believed the number of initial value x (0), y (0), z (0), w (0) or value of feedback
Number, transmitted in internal bus, into state machine, fixed-point number computing circuit to the digital signal of input carry out corresponding addition,
Multiplication obtains digital chaos signal x (k), y (k), z (k), the w (k) at k moment, and the digital chaos signal at k moment is through output bus
Circuit output, and simultaneously using the digital chaos signal at k moment as value of feedback be transmitted to conservative hyperchaotic system circuit carry out it is next
Secondary interative computation obtains subsequent time, i.e. digital chaos signal x (k+1), y (k+1), z (k+1), the w (k+1) at k+1 moment.
4. in the chaotic signal x (k), y (k), z (k), w (k) and dissipation hyperchaotic system (1) in present embodiment " x,
Y, z, w " physical meaning are identical, are all the state variables for indicating chaos equation, the former is discrete variable, and the latter is continuously to become
Amount.That is state variable x (k) is the discrete form of state variable x, that is, digital chaos signal.The change at x (k) expression k moment
Amount, that is, the first via digital chaos signal at k moment, x (k+1) indicate the variable at the subsequent time k+1 moment of k, that is, k
The first via digital chaos signal at+1 moment.Y (k) indicates that the second railway digital chaotic signal at k moment, y (k+1) indicate under k
The second railway digital chaotic signal at one moment at moment k+1.Similarly, z (k), w (k) respectively indicate the third road at k moment, the 4th tunnel
Digital chaos signal, z (k+1), w (k+1) respectively indicate the third road at k+1 moment, the 4th railway digital chaotic signal.
Claims (7)
1. a kind of building of the dissipation hyperchaotic system of double-wing chaotic attractor and its circuit are realized, which is characterized in that a kind of double-vane suction
The mathematical model of the dissipation hyperchaotic system of introduction are as follows:
Wherein x, y, z, w are variable, and a, b, c are real number.
2. a kind of building of the dissipation hyperchaotic system of double-wing chaotic attractor and its circuit are realized, which is characterized in that work as a=5, b=
When 10, c=3, the equation of system (1) becomes:
Taking initial value is [1,1,1,1], and system has double-wing chaotic attractor, and 4 Lyapunov indexes are respectively L1=
0.2625、L2=0.0632, L3=0.0034 and L4=-12.8214, the Lyapunov dimension of system are DL=2.0257；Thus
As it can be seen that system tool is dimension there are two positive Lyapunov index and Lyapunov dimension, so that verifying system is a consumption
Dissipate hyperchaotic system.
3. a kind of building of the dissipation hyperchaotic system of double-wing chaotic attractor and its circuit are realized, which is characterized in that using linear electricity
Resistance, capacitor, LM2924N type operational amplifier and MULTIPLIER analog multiplier, to have devised a simulation electronic electricity
Road；According to Analogical Electronics figure and Circuit theory, circuit equation is obtained are as follows:
4. a kind of building of the dissipation hyperchaotic system of double-wing chaotic attractor and its circuit are realized, which is characterized in that FPGA is realized will
Formula (1) Euler's formula discretization, obtains the discretization equation of dissipation hyperchaotic system are as follows:
Wherein, h is discrete sampling time step.
5. a kind of building of the dissipation hyperchaotic system of double-wing chaotic attractor and its circuit are realized, which is characterized in that use limited shape
State machine realize formula (4), and in order to reduce the consumption of hardware resource and improve system performance using fixed-point number operation and
It is not floating point arithmetic.
6. a kind of building of the dissipation hyperchaotic system of double-wing chaotic attractor and its circuit are realized, which is characterized in that the FPGA is real
Existing circuit includes dissipation hyperchaotic system module, key module, data output selecting module, D/A converter module and AD9767 group
At；Dissipation hyperchaotic system module realizes chaos system；Key module generates control signal, exports selecting module for data；
Data output selecting module selects two paths of signals to export from the four road signals that conservative hyperchaotic system module exports；Digital-to-analogue conversion
Module being capable of received signal for output signal to be converted to AD9767；AD9767 is used for dissipation hyperchaotic system module is defeated
Two-way output out is converted into analog signal so as to oscillograph observation.
7. a kind of building of the dissipation hyperchaotic system of double-wing chaotic attractor according to claim 6 and its circuit are realized,
It is characterized in that, what dissipation hyperchaotic system exported is the digital signal to initial value x (0), y (0), z (0), w (0) or value of feedback,
It is transmitted in internal bus, into state machine, fixed-point number computing circuit carries out corresponding addition, multiplication to the digital signal of input
Digital chaos signal x (k), y (k), z (k), the w (k) at k moment are obtained, the digital chaos signal at k moment is through output bus circuit
Output, and the digital chaos signal at k moment is transmitted to dissipation hyperchaotic system circuit as value of feedback simultaneously and is carried out next time
Interative computation obtains subsequent time, i.e. digital chaos signal x (k+1), y (k+1), z (k+1), the w (k+1) at k+1 moment.
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