CN109462467A - A kind of four dimensional chaos system containing hiding attractor and its realize circuit - Google Patents
A kind of four dimensional chaos system containing hiding attractor and its realize circuit Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
Abstract
The present invention discloses a kind of four dimensional chaos system containing hiding attractor and its realizes circuit.The system can also generate chaos attractor without equalization point excitation, its domain of attraction is present in the attraction basin not intersected with any equalization point, the potential function for having hiding system, change system initial value, chaotic motion track different, that variation is extremely complex can be obtained, which greatly improves the antidecoding capabilities of system, are suitably applied in secret communication and other encryption technologies.Due to hiding attractor chaos system to initial value and its sensitivity, physical model is difficult to realize, the present invention is realized using discrete analog device containing the chaotic oscillation system for hiding attractor, the circuit system can realize stable chaotic oscillation behavior without given initial value, provide physics implemented method for the application containing hiding attractor chaos system.
Description
Technical field
It the present invention relates to a kind of four dimensional chaos system containing hiding attractor and realizes circuit, belongs to chaotic signal
Generator circuit design field.
Background technique
The self-excitation attractor contained in classical Lorenz, Chen and Lu chaos system can be calculated by numerical value,
This kind of attractor is located in the neighborhood of its unstable equilibrium point, and the one kind found in recent years hides attractor, and domain of attraction can not
It is calculated in advance, more complicated nonlinear motion track is shown for different original states, belonged to and unlimited more suctions coexist
More stable states of introduction.
Due to can produce the motion profile and multistable state property that are more difficult to expect containing the chaos system for hiding attractor, more
It is suitably applied in chaotic secret communication, realizes that containing the chaos system for hiding attractor be chaos using simple analog device
Engineer application lays the foundation, and has good application value.
Summary of the invention
The object of the present invention is to provide a kind of four dimensional chaos system containing hiding attractor and realize circuit, system is one
The novel chaos system of kind, system realize that circuit parameter is easy to deploy, and generated chaotic signal has extremely strong pseudo-randomness.
The technical solution adopted by the present invention are as follows:
1. a kind of four-dimensional chaos system and its oscillating circuit containing hiding attractor, which is characterized in that including following step
It is rapid:
Chaos system mathematical model containing hiding attractor are as follows:
X, y, z in (I) formula, w are system state variables, and equalization point is not present in system (I), work as a=1, when b=0.05,
Liapunov exponent is LE1=0.012865, LE2=-0.0050839, LE3=-0.0098453, LE4=-0.033262,
Have a positive Liapunov exponent, and four Liapunov exponents and be negative, illustrate that system is convergent chaos
System.
In system (I), work as a=1, when b=0.05, state variable x, y, z and w is done substitution of variable, enable x=ux, y=uy,
Z=uz, w=uw, have:
Time change is carried out, t=τ is enabled0τ is enabledThen (II) formula becomes:
Circuit equation is designed by (III), enables R0=R4=R10=R17=R23, C0=C1=C2=C3=C4, have:
In order to make the corresponding parameter matching of system (II) and system (IV), in system (IV), resistance, capacitor and multiplier
Value are as follows: R1=R=R=R3=R=10K4Ω,9R13=R16=R17=R20=R22=R23=10K Ω, R2=R8=R14=R15
=R21=1K Ω, R7=200K Ω, C1=C2=C3=C4=1000nF, analog multiplier gain M1=M2=M3=M4=M5=
0.1, in addition, it is R that the system, which also needs parameter,5=R6=R11=R12=R18=R19The resistance and operational amplifier group of=10K Ω
It closes and constitutes voltage inverter.
2. realizing circuit containing the four dimensional chaos system for hiding attractor, circuit realization is made of four channel circuits.
First passage circuit is made of anti-analog multiplier M1, operational amplifier A1, operational amplifier A2 and capacitor C1
The phase inverter and resistance R1, resistance R2, resistance R3, resistance R4, resistance R5, resistance that phase integral device, operational amplifier A3 are constituted
R6 composition, the reverse phase integral that second channel circuit is made of multiplier M2, operational amplifier A4, operational amplifier A5 and capacitor C2
The phase inverter and resistance R7, resistance R8, resistance R9, resistance R10, resistance R11, resistance R12 group that device, operational amplifier A6 are constituted
At third channel circuit is by 1V DC voltage source, multiplier M3, multiplier M4, operational amplifier A7, operational amplifier A8 and electricity
Hold phase inverter and resistance R13, resistance R14, resistance R15, resistance that inverting integrator, the operational amplifier A9 that C3 is constituted are constituted
R16, resistance R17, resistance R18, resistance R19 composition, fourth lane circuit is by multiplier M5, operational amplifier A10, operation amplifier
Inverting integrator and resistance R20, resistance R21, resistance R22, the resistance R23 composition of device A11 and capacitor C4 composition.
The output signal of first passage circuit is ux, uxSignal and third channel output signal uzCollectively as multiplier M1
Input signal, input signal of the output end connection resistance R2 as first passage of M1 act in first passage circuit and transport
Calculate the inverting input terminal of amplifier A1, uxSignal becomes-u after passing through resistance R5 connection phase inverter A3xSignal ,-uxSignal connection electricity
Resistance R7 acts on the inverting input terminal of operational amplifier A4 in second channel circuit ,-uxSignal and uxSignal is collectively as multiplier
The input signal of M3, the output end of M3 act on operational amplifier A7 by input signal of the resistance R14 as third paths
Inverting input terminal.
The output signal of second channel circuit is uy, uySignal connects input signal of the resistance R1 as first passage, effect
The inverting input terminal of operational amplifier A1, u in first passage circuitySignal and third channel output signal uzCollectively as multiplying
The input signal of musical instruments used in a Buddhist or Taoist mass M2, input signal of the output signal connection resistance R8 of M2 as second channel, acts on second channel
The inverting input terminal of operational amplifier A4, u in circuitySignal becomes-u after passing through resistance R11 connection phase inverter A6ySignal ,-uy
Signal and uySignal is collectively as the input signal of multiplier M4, and the output end connection resistance R15 of M4 is as the defeated of third channel
Enter signal, acts on the inverting input terminal of operational amplifier A7.
The output signal of third channel circuit is uz, uzSignal and fourth lane output signal uwCollectively as multiplier M5
Input signal, input signal of the output end connection resistance R21 as fourth lane of M5 act on operational amplifier A10's
Inverting input terminal, uzSignal becomes-u after passing through resistance R18 connection phase inverter A9zSignal ,-uzSignal connects resistance R20 as the
The input signal of four-way, acts on the inverting input terminal of operational amplifier A10, and 1V DC voltage source connects resistance R13 conduct
Third channel input signal acts on the inverting input terminal of operational amplifier A7.
The output signal of fourth lane circuit is uw。
All operational amplifier in-phase end ground connection, all operational amplifier power supply negative terminal mouths connect -12V electricity in four channels
Pressure, operational amplifier power positive end mouth connect 12V voltage.
The inverting input terminal and output end of resistance R3 connection operational amplifier A1 in first passage, capacitor C1 connection operation are put
The inverting input terminal and output end of big device A2, the inverting input terminal and output end of resistance R6 connection operational amplifier A3.
In second channel, the inverting input terminal and output end of resistance R9 connection operational amplifier A4, capacitor C2 connection operation
The inverting input terminal and output end of amplifier A5, the inverting input terminal and output end of resistance R12 connection operational amplifier A6.
In third channel, the inverting input terminal and output end of resistance R16 connection operational amplifier A7, capacitor C3 connection operation
The inverting input terminal and output end of amplifier A8, the inverting input terminal and output end of resistance R19 connection operational amplifier A9.
In fourth lane, the inverting input terminal and output end of resistance R22 connection operational amplifier A10, capacitor C4 connection fortune
Calculate the inverting input terminal and output end of amplifier A11.
The beneficial effects of the present invention are: propose a kind of four dimensional chaos system containing hiding attractor and realize circuit,
The type containing the chaos system for hiding attractor is increased, is laid the foundation for the concrete application of chaos system.
Chaos system containing hiding attractor has multistable state property, and system motion track is difficult in the case of different initial values
Prediction, the pseudo-randomness of signal is extremely strong, realizes that circuit usually requires to disconnect and be closed repeatedly the switch of power supply to obtain
After certain initial value, chaos state just can enter.
The invention has the advantages that expanding containing hiding attractor chaos system type, voltage generation circuit is not required to obtain
Specific initial value can realize that chaotic oscillation, implementation are simple and reliable.
Detailed description of the invention
Fig. 1 is that a kind of four dimensional chaos system containing hiding attractor of the invention realizes circuit diagram.
Fig. 2 is the Liapunov exponent figure containing the four dimensional chaos for hiding attractor of the invention.
Fig. 3 is the two-dimensional simulation phasor of system of the invention (I).Wherein Fig. 3 (a) is y-x plane phasor, and Fig. 3 (b) is x-
Z-plane phasor, Fig. 3 (c) are y-z plane phasor, and Fig. 3 (d) is y-w plane phasor, and Fig. 3 (e) is x-w plane phasor, Fig. 3 (f)
For z-w plane phasor.
Fig. 4 is the circuit oscillograph observation experiment phasor of the corresponding circuit system (IV) of system of the invention (I), wherein scheming
4 (a) be uy-uxPlane phasor, Fig. 4 (b) are ux-uzPlane phasor, Fig. 4 (c) are uy-uzPlane phasor, Fig. 4 (d) are uy-uwIt is flat
Face phasor, Fig. 4 (e) are ux-uwPlane phasor, Fig. 4 (f) are uz-uwPlane phasor.
Specific embodiment
The present invention is described in further detail with reference to the accompanying drawing.
The present invention realizes goal of the invention using following technological means:
1. the construction one new four dimensional chaos system containing hiding attractor:
In (I) formula, x, y, z and w are four state variables, and a and b are system parameters, work as a=1, and when b=0.05, (I) is
Chaos system.
Equalization point is not present without solution, system in (I) system.
Fig. 2 shows the Liapunov exponent figure containing the four dimensional chaos for hiding attractor of the invention, (I) system Lee
Ya Punuofu index is LE1=0.012865, LE2=-0.0050839, LE3=-0.0098453, LE4=-0.033262, has
One positive Liapunov exponent, and four Liapunov exponents and be negative, it was demonstrated that the system (I) invented is to receive
The chaos system held back.
Fig. 3 shows the Matlab two-dimensional simulation phasor that invented system (I) uses the Ode45 algorithm solution differential equation,
System initial value is [- 1, -1,0,0], simulation step length 0.01.
Fig. 3 (a) is system (I) in y-x plane phasor, visible in y-x plane projection (- 6,6) and (- 5,5) space from scheming
In range, the infinite folding of motion profile and stretching of system (I), due to system be not present equalization point, attract basin not with balance
Point intersection, system (I) are the chaos system containing hiding attractor.
Fig. 3 (b) is system (I) in x-z-plane phasor, within the scope of x-z-plane (- 5,5) and (- 6,6) phase space, system
The Trajectory of (I) be the distinctive double scroll type attractors of chaos system, due to system be not present equalization point, attract basin not with
Equalization point intersection, system (I) are the chaos system containing hiding attractor.
Fig. 3 (c) is system (I) in y-z plane phasor, projects in (- 6,6) and (- 6,6) spatial dimension in y-z plane, is
Trajectory of uniting is to be similar to spherical double scroll shapes, the labyrinth with infinite nesting, since there is no balances for system
Point attracts basin not intersect with equalization point, and system (I) is the chaos system containing hiding attractor.
Fig. 3 (d) is system (I) in y-w plane phasor, y-w planar system Trajectory closely in occupation of (- 6,6) and (0,
20) finite spatial extent has self similarity shape but with converging at infinity, since equalization point is not present in system, attract basin not with put down
Weighing apparatus point intersection, system (I) is the chaos system containing hiding attractor.
Fig. 3 (e) is that system (I) is in x-w plane projection (- 5,5) and (0,20) spatial dimension in x-w plane phasor
System realizes exponent separation, the infinite folding of tracks and distortion in limited geometric object, since equalization point is not present in system,
It attracts basin not intersect with equalization point, and system (I) is the chaos system containing hiding attractor.
Fig. 3 (f) is that system (I) is in z-w plane projection (- 6,6) and (0,20) spatial dimension in z-w plane phasor
System Trajectory is infinite multiple screw structures, the attractor of the distinctive single scroll shape of chaos is showed, since system is not deposited
In equalization point, basin is attracted not intersect with equalization point, system (I) is the chaos system containing hiding attractor.
For the ease of circuit realization, work as a=1, when b=0.05, system (I) state variable x, y, z and w are done into variable generation
It changes, enables ux=x, uy=y, uz=z, uw=w, then have:
According to two-dimensional simulation phase Fig. 3 of system (I) it is found that Partial Variable range exceeds the linear region of operational amplifier,
Therefore system (I) is subjected to time compressed transform, enable t=τ0τ is enabledThen (II) formula becomes:
Equation is realized by the circuit of (III) designing system (I), enables R0=R4=R10=R17=R23, C0=C1=C2=C3=
C4, have:
In order to match the correspondence parameter of system (IV) and system (I), wherein two variables are multiplied using analog multiplier reality
It is existing, in system (IV), component parameter value are as follows: R1=R3=R4=R9=R10=10K Ω, R13=R16=R17=R20=
R22=R23=10K Ω, R2=R8=R14=R15=R21=1K Ω, R7=200K Ω, C1=C2=C3=C4=1000nF, simulation
Multiplier gain M1=M2=M3=M4=M5=0.1, in addition, it is R that the system, which also needs parameter,5=R6=R11=R12=R18=
R19The resistance of=10K Ω is combined with operational amplifier constitutes voltage inverter.
2. Fig. 1 is shown containing the four dimensional chaos system signal generator circuit for hiding attractor, Experiment of Electrical Circuits is in NI
Circuit is carried out on Multisim14.0 platform to build, circuit is made of four channel circuits, and first, second, third and the
The integrating circuit of four-way realizes the u of system (II) respectivelyx、uy、uzAnd uwThis four functions.
First passage circuit is made of anti-analog multiplier M1, operational amplifier A1, operational amplifier A2 and capacitor C1
The phase inverter and resistance R1, resistance R2, resistance R3, resistance R4, resistance R5, resistance that phase integral device, operational amplifier A3 are constituted
R6 composition, the reverse phase integral that second channel circuit is made of multiplier M2, operational amplifier A4, operational amplifier A5 and capacitor C2
The phase inverter and resistance R7, resistance R8, resistance R9, resistance R10, resistance R11, resistance R12 group that device, operational amplifier A6 are constituted
At third channel circuit is by 1V DC input voitage source, multiplier M3, multiplier M4, operational amplifier A7, operational amplifier A8
With capacitor C3 constitute inverting integrator, operational amplifier A9 constitute phase inverter and resistance R13, resistance R14, resistance R15,
Resistance R16, resistance R17, resistance R18, resistance R19 composition, fourth lane circuit is by multiplier M5, operational amplifier A10, operation
Inverting integrator and resistance R20, resistance R21, resistance R22, the resistance R23 composition of amplifier A11 and capacitor C4 composition.
The output signal of first passage circuit is ux, uxSignal and third channel output signal uzCollectively as multiplier M1
Input signal, input signal of the output end connection resistance R2 as first passage of M1 act in first passage circuit and transport
Calculate the inverting input terminal of amplifier A1, uxSignal becomes-u after passing through resistance R5 connection phase inverter A3xSignal ,-uxSignal connection electricity
Resistance R7 acts on the inverting input terminal of operational amplifier A4 in second channel circuit ,-uxSignal and uxSignal is collectively as multiplier
The input signal of M3, the output end of M3 act on operational amplifier A7 by input signal of the resistance R14 as third paths
Inverting input terminal, the inverting input terminal and output end of resistance R3 connection operational amplifier A1, capacitor C1 connection in first passage
The inverting input terminal and output end of operational amplifier A2, the inverting input terminal and output end of resistance R6 connection operational amplifier A3.
The output signal of second channel circuit is uy, uySignal connects input signal of the resistance R1 as first passage, effect
The inverting input terminal of operational amplifier A1, u in first passage circuitySignal and third channel output signal uzCollectively as multiplying
The input signal of musical instruments used in a Buddhist or Taoist mass M2, input signal of the output signal connection resistance R8 of M2 as second channel, acts on second channel
The inverting input terminal of operational amplifier A4, u in circuitySignal becomes-u after passing through resistance R11 connection phase inverter A6ySignal ,-uy
Signal and uySignal is collectively as the input signal of multiplier M4, and the output end connection resistance R15 of M4 is as the defeated of third channel
Enter signal, acts on the inverting input terminal of operational amplifier A7, the inverting input terminal of resistance R9 connection operational amplifier A4 and defeated
Outlet, the inverting input terminal and output end of capacitor C2 connection operational amplifier A5, the reverse phase of resistance R12 connection operational amplifier A6
Input terminal and output end.
The output signal of third channel circuit is uz, uzSignal and fourth lane output signal uwCollectively as multiplier M5
Input signal, input signal of the output end connection resistance R21 as fourth lane of M5 act on operational amplifier A10's
Inverting input terminal, uzSignal becomes-u after passing through resistance R18 connection phase inverter A9zSignal ,-uzSignal connects resistance R20 as the
The input signal of four-way, acts on the inverting input terminal of operational amplifier A10, and 1V DC voltage source connects resistance R13 conduct
Third channel input signal acts on the inverting input terminal of operational amplifier A7, the reverse phase of resistance R16 connection operational amplifier A7
Input terminal and output end, the inverting input terminal and output end of capacitor C3 connection operational amplifier A8, resistance R19 connection operation amplifier
The inverting input terminal and output end of device A9.
The output signal of fourth lane circuit is uw, the inverting input terminal and output of resistance R22 connection operational amplifier A10
End, the inverting input terminal and output end of capacitor C4 connection operational amplifier A11.
All operational amplifier in-phase end ground connection, all operational amplifier power supply negative terminal mouths connect -12V electricity in four channels
Pressure, operational amplifier power positive end mouth connect 12V voltage.
In the four-dimension containing hiding in attractor chaos system signal generator circuit, operational amplifier uses TL082, multiplication
Device uses gain for 0.1 AD633, selects linear resistance and capacitor.
Fig. 4 show the corresponding circuit of system of the invention (I) realize system (IV) based on NI Multisim 14.0
Experiment of Electrical Circuits phasor.
Fig. 4 (a) is the u observed with oscillography-uxPlane phasor, from figure as it can be seen that in a limited space in range, system
The infinite folding of the motion profile of (IV) and stretching, system are chaos system.
Fig. 4 (b) is the u observed with oscillographx-uzPlane phasor, from figure as it can be seen that system motion path is chaos system
Distinctive double scroll type attractors, system work in chaos state.
Fig. 4 (c) is the u observed with oscillography-uzPlane phasor, from figure as it can be seen that system motion path is to be similar to ball
Double scroll shapes of shape, system are chaos system.
Fig. 4 (d) is the u observed with oscillography-uwPlane phasor, from figure as it can be seen that in a limited space in range, system
Trajectory has self similarity shape but with converging at infinity, and system is chaos system.
Fig. 4 (e) is the u observed with oscillographx-uwPlane phasor, from figure as it can be seen that in a limited space in range, system
The infinite folding of tracks and distortion, converge at infinity, and system is chaos system.
Fig. 4 (f) is the u observed with oscillographz-uwPlane phasor, from figure as it can be seen that in a limited space in range, system
Tracks are the attractor of single scroll shape, and system is chaos system.
It is right from Fig. 3 institute that can be seen that circuit implementations and Numerical Simulation Results with oscillograph observation two dimension phasor Fig. 4
The each variable answered is almost the same, it was demonstrated that the realization circuit containing the four dimensional chaos system for hiding attractor that the present invention is constructed
With theoretical foundation and reliable physical realizability.
A kind of provided four dimensional chaos system containing hiding attractor and corresponding signal are implemented to the present invention above
Circuit occurs to be described in detail, above description is not the limitation to invention, and the present invention is also not limited to the example above, this skill
The variations, modifications, additions or substitutions that the those of ordinary skill in art field is made within the essential scope of the present invention also belong to this
The protection scope of invention.
Claims (3)
1. a kind of four dimensional chaos system containing hiding attractor and its realization circuit, it is characterized in that being, comprising the following steps:
It is (1) four-dimensional to contain the chaos system for hiding attractor are as follows:
In (I) formula, x, y, z and w are four state variables, and equalization point is not present in system (I), work as a=1, when b=0.05, Lee
Ya Punuofu index is LE1=0.012865, LE2=-0.0050839, LE3=-0.0098453, LE4=-0.033262, has
One positive Liapunov exponent, and four Liapunov exponents and be negative, illustrate that system is convergent chaos system
System.
(2) in system (I), work as a=1, when b=0.05, state variable x, y, z and w are done substitution of variable, enable x=ux, y=uy, z
=uz, w=uw, have:
(3) time change is carried out, t=τ is enabled0τ is enabledThen (II) formula becomes:
(4) circuit equation is designed by (III), enables R0=R4=R10=R17=R23, C0=C1=C2=C3=C4, have:
In system (IV), the value of resistance, capacitor and multiplier are as follows: R1=R3=R4=R9=R10=10K Ω, R13=R16=
R17=R20=R22=R23=10K Ω, R2=R8=R14=R15=R21=1K Ω, R7=200K Ω, C1=C2=C3=C4=
1000nF, analog multiplier gain M1=M2=M3=M4=M5=0.1, in addition, it is R that the system, which also needs parameter,5=R6=R11
=R12=R18=R19The resistance of=10K Ω is combined with operational amplifier constitutes voltage inverter.
(5) it is made of containing attractor chaos system is hidden four channel circuits using system (IV) construction, first passage circuit
Inverting integrator, the operational amplifier A3 being made of analog multiplier M1, operational amplifier A1, operational amplifier A2 and capacitor C1
The phase inverter and resistance R1 of composition, resistance R2, resistance R3, resistance R4, resistance R5, resistance R6 composition, second channel circuit by
Inverting integrator that multiplier M2, operational amplifier A4, operational amplifier A5 and capacitor C2 are constituted, operational amplifier A6 are constituted
Phase inverter and resistance R7, resistance R8, resistance R9, resistance R10, resistance R11, resistance R12 composition, third channel circuit are straight by 1V
Inverting integrator that galvanic electricity potential source, multiplier M3, multiplier M4, operational amplifier A7, operational amplifier A8 and capacitor C3 are constituted,
Operational amplifier A9 constitute phase inverter and resistance R13, resistance R14, resistance R15, resistance R16, resistance R17, resistance R18,
Resistance R19 composition, fourth lane circuit are made of multiplier M5, operational amplifier A10, operational amplifier A11 and capacitor C4
Inverting integrator and resistance R20, resistance R21, resistance R22, resistance R23 composition；
The output signal of first passage circuit is ux, uxSignal and third channel output signal uzCollectively as the defeated of multiplier M1
Enter signal, input signal of the output end connection resistance R2 of M1 as first passage acts on operation in first passage circuit and put
The inverting input terminal of big device A1, uxSignal becomes-u after passing through resistance R5 connection phase inverter A3xSignal ,-uxSignal connects resistance R7
Act on the inverting input terminal of operational amplifier A4 in second channel circuit ,-uxSignal and uxSignal is collectively as multiplier M3's
Input signal, the output end of M3 act on the anti-of operational amplifier A7 by input signal of the resistance R14 as third paths
Phase input terminal；
The output signal of second channel circuit is uy, uySignal connects input signal of the resistance R1 as first passage, acts on the
The inverting input terminal of operational amplifier A1, u in one channel circuitySignal and third channel output signal uzCollectively as multiplier
The input signal of M2, input signal of the output signal connection resistance R8 of M2 as second channel, acts on second channel circuit
The inverting input terminal of middle operational amplifier A4, uySignal becomes-u after passing through resistance R11 connection phase inverter A6ySignal ,-uySignal
With uyInput signal of the signal collectively as multiplier M4, input letter of the output end connection resistance R15 of M4 as third channel
Number, act on the inverting input terminal of operational amplifier A7；
The output signal of third channel circuit is uz, uzSignal and fourth lane output signal uwCollectively as the defeated of multiplier M5
Enter signal, input signal of the output end connection resistance R21 of M5 as fourth lane acts on the reverse phase of operational amplifier A10
Input terminal, uzSignal becomes-u after passing through resistance R18 connection phase inverter A9zSignal ,-uzSignal connects resistance R20 as four-way
The input signal in road, acts on the inverting input terminal of operational amplifier A10, and 1V DC voltage source connects resistance R13 as third
Channel input signal acts on the inverting input terminal of operational amplifier A7；
The output signal of fourth lane circuit is uw；
All operational amplifier in-phase end ground connection, all operational amplifier power supply negative terminal mouths connect -12V voltage, transport in four channels
It calculates the positive port of APS amplifier power supply and connects 12V voltage.
2. a kind of four-dimensional chaos system containing hiding attractor according to claim 1 and its realization circuit, feature
It is: the inverting input terminal and output end of resistance R3 connection operational amplifier A1 in first passage, capacitor C1 connection operation amplifier
The inverting input terminal and output end of device A2, the inverting input terminal and output end of resistance R6 connection operational amplifier A3；Second channel
In, the reverse phase of the inverting input terminal and output end of resistance R9 connection operational amplifier A4, capacitor C2 connection operational amplifier A5 is defeated
Enter end and output end, the inverting input terminal and output end of resistance R12 connection operational amplifier A6；In third channel, resistance R16 connects
Connect the inverting input terminal and output end of operational amplifier A7, the inverting input terminal and output of capacitor C3 connection operational amplifier A8
End, the inverting input terminal and output end of resistance R19 connection operational amplifier A9；In fourth lane, resistance R22 connection operation amplifier
The inverting input terminal and output end of device A10, the inverting input terminal and output end of capacitor C4 connection operational amplifier A11.
3. a kind of four-dimensional chaos system containing hiding attractor according to claim 1 and its realization circuit, feature
Be: the operational amplifier is all made of TL082, and the multiplier is all made of the AD633 that gain is 0.1.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811630417.0A CN109462467B (en) | 2018-12-29 | 2018-12-29 | Four-dimensional chaotic system containing hidden attractor and implementation circuit thereof |
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| Application Number | Priority Date | Filing Date | Title |
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| CN201811630417.0A CN109462467B (en) | 2018-12-29 | 2018-12-29 | Four-dimensional chaotic system containing hidden attractor and implementation circuit thereof |
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