CN109407550A - A kind of building and its FPGA circuitry realization of conservative hyperchaotic system - Google Patents
A kind of building and its FPGA circuitry realization of conservative hyperchaotic system Download PDFInfo
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Abstract
The present invention relates to a kind of buildings of conservative hyperchaotic system and its FPGA to realize.There is conservative chaotic motion and the movement of conservative hyperchaos in a wide range of and a small range respectively in conservative hyperchaotic system proposed by the present invention, and the phenomenon that being coexisted there are infinite track, therefore system has complicated kinetic characteristics, and the application in information security has apparent advantage.FPGA realizes that circuit includes conservative hyperchaotic system module, key module, data output selecting module, D/A converter module and AD9767 composition.Conservative 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；D/A converter module being capable of received signal for output signal to be converted to AD9767；AD9767 converts analog signal for the two-way output that conservative hyperchaotic system module exports so as to oscillograph observation.
Description
Technical field
The present invention relates to a kind of chaos system and its circuit, in particular to the building of a kind of conservative hyperchaotic system and its
FPGA circuitry is realized.
Background technique
Currently, people, which are mainly reflected in construction to the research of conservative chaos system, is different from the conservative mixed of Sprott-A system
Ignorant system.These differences are mainly reflected in balance vertex type, on biggish positive Lyapunov index.However, with dissipation
Chaos system is compared, require study in conservative chaos system there are also other characteristics, as hyperchaos, chaotic orbit coexisting and coexisting
Number and the shape of chaotic orbit etc..The invention proposes a kind of buildings of conservative hyperchaotic system and its FPGA circuitry to realize,
It is applied to the engineering fields such as communication for chaos system and provides a kind of new method and thinking.
Summary of the invention
The purpose of the present invention is construct a kind of conservative hyperchaotic system and its FPGA circuitry.With known conservative chaos system
It compares, the dynamic behavior of the conservative hyperchaotic system is increasingly complex, therefore the application in information security is with apparent excellent
Gesture.
The technical solution adopted by the present invention to solve the above technical problem is:
1. a kind of construction method of conservative hyperchaotic system, it is characterised in that the following steps are included:
The mathematical model of conservative hyperchaotic system are as follows:
Wherein x, y, z, w are variable, and c is real number.
Compared with known conservative chaos system, which is had the following characteristics that
1) therefore system exists without equalization point hides chaotic orbit.
2) when c ∈ [- 60,60], system is Conservative Systems.
3) when c ∈ [0,5], system is in conservative hyperchaos state；When c ∈ [- 60,0) ∪ (5,60], system is in
Conservative chaos state.
4) when to system different initial value, there are infinite tracks, and phenomenon coexists for system.
2. a kind of building of conservative hyperchaotic system and its FPGA circuitry are realized, it is characterised in that the following steps are included:
The FPGA of the conservative hyperchaotic system realizes that circuit includes conservative hyperchaotic system module, key module, data
Export selecting module, D/A converter module and AD9767 composition.Conservative hyperchaotic system module realizes chaos system；Key module
Control signal is generated, exports selecting module for data；Data output selecting module is exported from conservative hyperchaotic system module
Two paths of signals output is selected in four road signals；D/A converter module received can be believed for output signal to be converted to AD9767
Number；AD9767 is the parallel D/A converter module with the 14bit bit wide of two-way, by the two of the output of conservative hyperchaotic system module
Road output is converted into analog signal so as to oscillograph observation.
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:
Lyapunov exponential spectrum when Fig. 1 is [- 60,60] c ∈ of the present invention；
Lyapunov exponential spectrum when Fig. 2 is [- 5,5] c ∈ of the present invention；
The sum of Lyapunov exponential spectrum when Fig. 3 is [- 60,60] c ∈ of the present invention and Lyapunov dimension；
The sum of Lyapunov exponential spectrum when Fig. 4 is [- 5,5] c ∈ of the present invention and Lyapunov dimension；
X-y, x-z, y-z, x-w, w-y, z-w phasor of MATLAB emulation when Fig. 5 is c=-3.25 of the present invention；
Fig. 6 is that conservative chaotic orbit coexists when chaotic orbit spacing of the present invention is close；
Fig. 7 is that conservative chaotic orbit far constantly coexists in chaotic orbit spacing of the present invention；
X-y, x-z, y-z, x-w, w-y, z-w phasor of MATLAB emulation when Fig. 8 is c=5 of the present invention；
Fig. 9 is that conservative hyperchaotic orbits coexist when hyperchaotic orbits spacing of the present invention is close；
Figure 10 is that conservative hyperchaotic orbits coexist when hyperchaotic orbits spacing of the present invention is remote；
Figure 11 is system block diagram of the invention；
Figure 12 is the state machine of the conservative hyperchaotic system of the present invention；
Figure 13 is the flow chart of sin function of the invention；
Figure 14 is the RTL figure that FPGA of the invention realizes system；
FPGA exports x-y, x-z, y-z, x-w, w-y, z-w phase that oscillograph captures when Figure 15 is c=-3.25 of the present invention
Figure；
FPGA exports x-y, x-z, y-z, x-w, w-y, z-w phasor that oscillograph captures when Figure 16 is c=5 of the present invention.
Specific embodiment
Hereinafter reference will be made to the drawings, and the present invention is described in detail.
Specific embodiment 1: present embodiment is described in detail for conservative hyperchaotic system proposed by the present invention:
1. the mathematical model of conservative hyperchaotic system are as follows:
Wherein x, y, z, w are variable, and c is real number.
2. the kinetic characteristics of conservative hyperchaotic system
(1) equalization point
The equalization point of system (1) can solve following Algebraic Equation set and obtain
Equation is without solution known to formula (2), i.e., conservative hyperchaotic system (1) is without equalization point.
(2) Lyapunov index and Lyapunov dimension
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
When initial value is [1,2,3,4], using classical Runge-Kutta algorithm, calculated using MATLAB software
It is as depicted in figs. 1 and 2 Lyapunov exponential spectrum difference of the system (1) in c ∈ [- 60,60] and [- 5,5] ∈ c has been obtained；c∈
The sum of Lyapunov index when [- 60,60] and [- 5,5] ∈ c is distinguished as shown in Figures 2 and 3 with Lyapunov dimension.
As can be seen from figs. 3 and 4 the sum of Lyapunov index of system is zero and Lyapunov is tieed up when c ∈ [- 60,60]
It is Conservative Systems that number, which is equal to system known to the dimension of system,.It is found that when working as [0,5] c ∈, system has two by complex chart 1 and Fig. 2 again
A positive Lyapunov index is in conservative hyperchaos state；When c ∈ [- 60,0) ∪ (5,60], system have one it is positive
Lyapunov index is in conservative chaos state.
(3) phenomenon coexists in infinite track
It is limited in a cycle function if primary and this variable only occurs in a variable, then specific at one
Can occur infinite multiple tracks under coordinate system to coexist.In system (1), it can be seen that w variable only existsOccur in equation primary
And be limited in a sin function, it may thus be appreciated that there are system (1) infinite multiple tracks to coexist.
Selection c=-3.25 and c=5 coexists phenomenon to track and analyzes below:
1) coexisting for chaotic orbit is guarded when c=-3.25
When initial value is [1,2,3,4], referred to using 4 Lyapunov that system (1) has been calculated in MATLAB software
Number is respectively L1=0.677, L2=0, L3=-0.136 and L4=-0.541, it is known that there is a positive Lyapunov index, this
When system be in conservative chaos state, phasor is as shown in Figure 5.
Take initial value be [1,2,3,0], [1,2,3,4], [1,2,3,20], [1,2,3, -6], [1,2,3, -10], [- 1, -
2, -3, -2], [- 1, -2, -1,12] and [- 1, -2, -1, -4], the conservative chaotic orbit coexisted is drawn using MATLAB software such as
Shown in Fig. 6, it can be seen that these tracks are close to each other.
Taking initial value is [1,2, m, 4] (m >=0), takes the value of 8 m, the conservative chaos coexisted is drawn using MATLAB software
Track is as shown in Figure 7, it can be seen that these interorbitals are away from increasingly remoter.
2) coexisting for hyperchaotic orbits is guarded when c=5
When initial value is [1,2,3,4], referred to using 4 Lyapunov that system (1) has been calculated in MATLAB software
Number is respectively L1=0.498, L2=0.154, L3=0 and L4=-0.652, it is known that have there are two positive Lyapunov index, this
When system be in conservative hyperchaos state, phasor is as shown in Figure 8.
Take initial value be [1,2,1.3,1], [1,2,2,1.6], [2,3,4,0], [- 1,0,1, -1], [3, -2, -0.8,
0.6], [3, -2, -1,0.1], [1,0, -1, -1.5] and [1,2,3,4], drawn using MATLAB software coexist it is conservative super mixed
Ignorant track is as shown in Figure 9, it can be seen that these tracks are close to each other.
Taking initial value is [m, 1,1,1] (m >=0), takes the value of 8 m, the conservative chaos coexisted is drawn using MATLAB software
Track is as shown in Figure 10, it can be seen that these interorbitals are away from increasingly remoter.
Specific embodiment 2: present embodiment for a kind of building of conservative hyperchaotic system proposed by the present invention and
FPGA circuitry realization is described in detail:
1. as shown in figure 11, present embodiment gives the system block diagram that the FPGA circuitry of conservative hyperchaotic system is realized,
The system block diagram is by conservative hyperchaotic system module, key module, data output selecting module, D/A converter module and AD9767
Composition.Conservative hyperchaotic system module realizes chaos system；Key module generates control signal, for data output selection mould
Block；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 the 14bit bit wide with two-way
Parallel D/A converter module, by conservative hyperchaotic system module output two-way output be converted into analog signal so as to oscillograph
Observation.
2. being as shown in figure 12 the state machine of conservative hyperchaotic system.Describing either conservative hyperchaotic system circuit is realized best
Method is use state machine, can describe multiple circuit modules parallel in each state, calculating process is divided into different steps
Suddenly, it is described in the different conditions of state machine respectively.The S0 state of beginning then branches to S1 state for initializing initial value；S1
State by x, y, z, w be updated to last iterative calculation as a result, then branching to S2 state；S2 state is used to add noise,
System is set to be in chaos state always, every iteration 3000 times additions are primary, i.e. add_noise 3000 assignment of every iteration are primary,
Other when be 0, then branch to S3 state；S3 state carries out fixed-point multiplication operation, then branches to S4 state；S4 state and
S5 state is all used for the result of S3 state computation multiplied by h (h=2-12), is in fact exactly that result is moved to right 12bit, then from S5
State transition is to S6 state；S6 state obtains the output of an iteration by fixed-point number additional calculation, then branches to S7 state；
S7 state is used to result cut position obtaining the output of 14bit, then branches to S1, carries out interative computation next time, thus one
Straight iteration continues, constantly generation result.
3. being as shown in figure 13 the flow chart of sin function, main function is to realize sin function by searching for table, due to w
(k) value is between -200 to 200, in order to save memory space, needs to go to the value of w (k) between 0-2 π (only of equal value
In this range, actually range is very big), it is also necessary to consider the problems of quadrant, result negates if in three four-quadrants.
4. writing program according to Figure 11-13, the RTL figure after full compiling is as shown in figure 14.It takes initial value [1,2,3,4], joins
When number c takes -3.25 and 5 respectively, the phasor that FPGA output captures on oscillograph is as shown in Figure 15 and Figure 16.5 He of comparison diagram
Fig. 8, it is known that the system phasor that FPGA is realized is consistent with the system phasor of MATLAB the Realization of Simulation.
Claims (7)
1. a kind of building of conservative hyperchaotic system and its FPGA circuitry are realized, which is characterized in that the number of conservative hyperchaotic system
Learn model are as follows:
Wherein x, y, z, w are variable, and c is real number.
2. a kind of building of conservative hyperchaotic system and its FPGA circuitry are realized, which is characterized in that with known conservative chaos system
System is compared, which has the following characteristics that
1) therefore system exists without equalization point hides chaotic orbit；
2) when c ∈ [- 60,60], system is Conservative Systems；
3) when c ∈ [0,5], system is in conservative hyperchaos state；When c ∈ [- 60,0) ∪ (5,60], system is in conservative
Chaos state；
4) when to system different initial value, there are infinite tracks, and phenomenon coexists for system.
3. a kind of building of conservative hyperchaotic system and its FPGA circuitry are realized, which is characterized in that by formula (1) with Euler's formula from
Dispersion obtains the discretization equation of conservative hyperchaotic system are as follows:
Wherein, h is discrete sampling time step.
4. a kind of building of conservative hyperchaotic system and its FPGA circuitry are realized, which is characterized in that realized using finite state machine
Formula (2), and in order to reduce the consumption of hardware resource and improve the performance of system using fixed-point number operation rather than floating-point
Number operation.
5. a kind of building of conservative hyperchaotic system and its FPGA circuitry are realized, which is characterized in that the FPGA realizes circuit packet
Include FPGA, clock circuit, reset circuit, ASP download interface, JTAG download interface, AD9767, key；FPGA is for generating four
Hyperchaotic system circuit is kept in maintenance；Clock circuit is used to provide clock signal for FPGA；Reset circuit is for resetting FPGA；
ASP download interface and JTAG download interface are connect on FPGA；Key is used to select the output of two-way chaotic signal；AD9767 is used for will
The two-way chaos digital signal of FPGA output is converted to analog signal.
6. a kind of building of conservative hyperchaotic system according to claim 5 and its FPGA circuitry are realized, which is characterized in that
What conservative hyperchaotic system exported is the digital signal to initial value x (0), y (0), z (0), w (0) or value of feedback, internal total
It is transmitted in line, into state machine, when fixed-point number computing circuit carries out corresponding addition to the digital signal of input, multiplication obtains n
Digital chaos signal x (n), y (n), z (n), the w (n) at quarter, the digital chaos signal at n moment through output bus circuit output, and
The digital chaos signal at n moment the iteration that conservative hyperchaotic system circuit carries out next time is transmitted to as value of feedback simultaneously to transport
It calculates, obtains subsequent time, i.e. digital chaos signal x (n+1), y (n+1), z (n+1), the w (n+1) at n+1 moment.
7. a kind of building of the conservative hyperchaotic system according to claim 5 and 6 and its FPGA circuitry realize that feature exists
In the FPGA development board of Xilinx model xc7z020clg400 and the parallel highest conversion rate of the twoport of model AD9767
The hardware platform formed for the D/A converter of 125Mhz；Software is Vivado 2016.4, and programming language is verilog hardware volume
Cheng Yuyan.
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| CN112422259A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | Generalized Sprott-A system with eight clusters of conservative chaotic streams and circuit implementation thereof |
| CN112422258A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | Improved Sprott-A system with single cluster of conservative chaotic streams and circuit implementation of improved Sprott-A system |
| CN112422262A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | Generalized Sprott-A system with double cluster conservative chaotic streams and circuit implementation thereof |
| CN112422261A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | Generalized Sprott-A system with four clusters of conservative chaotic streams and circuit implementation thereof |
| CN112929309A (en) * | 2021-01-19 | 2021-06-08 | 重庆邮电大学 | Large-range chaotic system and application thereof in DCSK (data communication phase Shift keying) |
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| CN112422259A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | Generalized Sprott-A system with eight clusters of conservative chaotic streams and circuit implementation thereof |
| CN112422258A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | Improved Sprott-A system with single cluster of conservative chaotic streams and circuit implementation of improved Sprott-A system |
| CN112422262A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | Generalized Sprott-A system with double cluster conservative chaotic streams and circuit implementation thereof |
| CN112422261A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | Generalized Sprott-A system with four clusters of conservative chaotic streams and circuit implementation thereof |
| CN112422262B (en) * | 2019-08-23 | 2022-05-20 | 天津科技大学 | Generalized Sprott-A system with double cluster conservative chaotic streams and construction method thereof |
| CN112422261B (en) * | 2019-08-23 | 2022-05-20 | 天津科技大学 | Generalized Sprotet-A system with four cluster conservative chaotic streams and construction method thereof |
| CN112422258B (en) * | 2019-08-23 | 2022-07-29 | 天津科技大学 | Construction method of improved Sprott-A system with single cluster of conservative chaotic streams |
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| CN112929309A (en) * | 2021-01-19 | 2021-06-08 | 重庆邮电大学 | Large-range chaotic system and application thereof in DCSK (data communication phase Shift keying) |
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