CN105681021B - A kind of chaos circuit of Three Dimensional Generalized dissipation Hamilton system - Google Patents
A kind of chaos circuit of Three Dimensional Generalized dissipation Hamilton system Download PDFInfo
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- CN105681021B CN105681021B CN201610210330.2A CN201610210330A CN105681021B CN 105681021 B CN105681021 B CN 105681021B CN 201610210330 A CN201610210330 A CN 201610210330A CN 105681021 B CN105681021 B CN 105681021B
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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
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Abstract
The present invention relates to a kind of chaos circuits of Three Dimensional Generalized dissipation Hamilton system, the circuit is made of three channel circuits: first passage circuit is made of multiplier, operational amplifier and resistance and capacitor, second channel circuit is made of operational amplifier and resistance and capacitor, and third channel is made of multiplier, DC power supply, operational amplifier and resistance and capacitor.The present invention only exists an equalization point；The dissipation characteristic of system not instead of constant, variable relevant to state variable；Chaos attractor existing for system is more much bigger than the Lyapunov dimension of known three-dimensional chaos attractor, the time series that the system generates is more much greater than the complexity for the time series that known chaos system generates, this has potential application in the field of information encryption based on chaotic signal.
Description
Technical field
The present invention relates to a kind of chaos systems and circuit to realize, in particular to a kind of Three Dimensional Generalized dissipation Hamilton system
Chaos circuit.
Background technique
Hamilton system is one very important research theme of nonlinear science field, is widely present in physics section
It learns, many in life science and field of engineering technology, especially classical mechanics, celestial mechanics, space science and bioengineering
Model has deep physical background all with the appearance of Hamilton system form, and classical Hamilton system is in even number
Phase space definition is tieed up, have the advantages that the system of this structure there are good property and facilitates research, but is mutually empty without odd number dimension
Between limit its scope of application, maintain system to enable Hamilton system to be applied to odd number, just there is Generalized Hamilton system
The it is proposed of system.Up to the present, the research achievement of the chaotic Property Analysis in Hamilton system and its chaos controlling is not very
More, this system can be stretched using energy dissipation in generalized dissipation Hamilton system and diffusion with the state trajectory in chaotic motion
It is corresponding with contraction, to excavate chaotic characteristic in generalized dissipation Hamilton system, broad sense is utilized on this basis
The characteristics of Hamilton system, constructs a kind of chaos system with dissipative structure, and combines a specific example to dynamics
Behavior is made explanations.
Summary of the invention
The technical problem to be solved in the present invention is to provide a kind of chaos circuits of Three Dimensional Generalized dissipation Hamilton system:
1. a kind of construction method of the chaos system of Three Dimensional Generalized dissipation Hamilton system, which is characterized in that including with
Lower step:
(1) Three Dimensional Generalized dissipation Hamilton chaos system (1) are as follows:
X in formula, y, z are state variable；
(2) circuit based on system (1) construction, it is characterised in that: the circuit is made of three channel circuits: first passage
Circuit by multiplier A3, operational amplifier U2C, operational amplifier U2B, operational amplifier U2A and resistance R15, resistance R14,
Resistance R7, resistance R8, resistance R9, resistance R4, resistance R1 and capacitor C1 composition, second channel circuit is by operational amplifier U3C, fortune
Calculate amplifier U3B, operational amplifier U3A and resistance R17, resistance R16, resistance R10, resistance R11, resistance R5, resistance R2 and
Capacitor C2 composition, third channel is by multiplier A2, DC power supply V1, operational amplifier U4C, operational amplifier U4B, operation amplifier
Device U4A and resistance R20, resistance R21, resistance R19, resistance R12, resistance R13, resistance R6, resistance R3 and capacitor C3 composition；The
The output signal feedback of one channel circuit connects resistance R15 as input signal, the output signal are also connected with all the way to input terminal
Multiplier A2 acts on third channel, which is also used as the input signal all the way of multiplier A3 in first passage circuit,
The output signal is also connected with resistance R17 and acts on second channel circuit；The output signal of second channel circuit is fed back to input terminal,
Connection resistance R8 acts on first passage, is also connected with resistance R20 and acts on third channel circuit；The output of third channel circuit is believed
Number feedback arrive input terminal, the output signal connection multiplier A3 act on first passage circuit, the output signal connect resistance R11
Act on second channel circuit；DC power supply V1 connection resistance R13 acts on third channel circuit.
2, multiplier A3 is connected by resistance R9 with the negative input end of operational amplifier U2B in the first passage circuit；
The negative input end of operational amplifier U2C is connected by resistance R14 with the output end of operational amplifier U2C；Operational amplifier U2C's
Positive input terminal ground connection；The output end of operational amplifier U2C is connected by resistance R7 with the negative input end of operational amplifier U2B；Fortune
The negative input end for calculating amplifier U2B is connected by resistance R4 with the output end of operational amplifier U2B；Operational amplifier U2B is just
Input end grounding；The output end of operational amplifier U2B is connected by resistance R1 with the negative input end of operational amplifier U2A；Operation
The negative input end of amplifier U2A is connected by capacitor C1 with the output end of operational amplifier U2A；Operational amplifier U2A's is just defeated
Enter end ground connection, positive power source terminal connection VCC, the negative power end of operational amplifier U2A connects VDD；The output end of operational amplifier U2A
It is connected by resistance R15 with the negative input end of operational amplifier U2C；The output end of operational amplifier U2A passes through resistance R17 and the
The negative input end of operational amplifier U3C in two channel circuits；In the output end connection third channel circuit of operational amplifier U2A
Multiplier A2 two input terminals；The output end of the U2A of operational amplifier connects the multiplier A3's in first passage circuit
One input terminal.
3, the negative input end of the operational amplifier U3C in the second channel circuit passes through resistance R16 and operational amplifier
The output end of U3C is connected；The positive input terminal of operational amplifier U3C is grounded；The output end of operational amplifier U3C passes through resistance R10
It is connected with the negative input end of operational amplifier U3B；The negative input end of operational amplifier U3B passes through resistance R5 and operational amplifier
The output end of U3B is connected；The positive input terminal of operational amplifier U3B is grounded；The output end of operational amplifier U3B by resistance R2 with
The negative input end of operational amplifier U3A is connected；The negative input end of operational amplifier U3A passes through capacitor C2 and operational amplifier U3A
Output end be connected；The positive input terminal of operational amplifier U3A is grounded；The positive supply of operational amplifier U3A terminates VCC, negative supply
Terminate VDD；The output end of operational amplifier U3A is defeated by resistance R8 and bearing for the operational amplifier U2B in first passage circuit
Enter end to be connected；The output end of operational amplifier U3A passes through the negative of the operational amplifier U4C in resistance R20 and third channel circuit
Input terminal is connected.
4, the multiplier A2 in the third channel circuit passes through the negative input end phase of resistance R21 and operational amplifier U4C
Even；The negative input end of operational amplifier U4C is connected by resistance R19 with the output end of operational amplifier U4C；Operational amplifier
The positive input terminal of U4C is grounded；The output end of operational amplifier U4C passes through the negative input end phase of resistance R12 and operational amplifier U4B
Even；The negative input end of operational amplifier U4B is connected by resistance R6 with the output end of operational amplifier U4B；Operational amplifier U4B
Positive input terminal ground connection；The output end of operational amplifier U4B is connected by resistance R3 with the negative input end of operational amplifier U4A；
The negative input end of operational amplifier U4A is connected by capacitor C3 with the output end of operational amplifier U4A；Operational amplifier U4A's
Positive input terminal ground connection；Positive supply termination VCC, the negative supply of operational amplifier U4A terminates VDD；The output end of operational amplifier U4A
Connect the other end of the multiplier A3 in first passage circuit；The output end of operational amplifier U4A is logical by resistance R11 and second
The negative input end of operational amplifier U3B in road circuit is connected；One end of DC power supply V1 is grounded；The other end of DC power supply V1
Pass through the negative input end of resistance R13 and operational amplifier U4B.
The utility model has the advantages that the present invention only exists an equalization point；The dissipation characteristic of system not instead of constant, with state variable
Relevant variable；Chaos attractor existing for system is more much bigger than the Lyapunov dimension of known three-dimensional chaos attractor,
That is the system generate time series it is more much greater than the complexity for the time series that known chaos system generates, this
Field of information encryption based on chaotic signal has potential application.
Detailed description of the invention
Fig. 1 is the schematic diagram of circuit connection structure of the preferred embodiment of the present invention.
Fig. 2 is the first, second and third channel timing diagram of present system in the present invention
Fig. 3 is X-Y phasor of the invention.
Fig. 4 is X-Z phasor of the invention.
Fig. 5 is Y-Z phasor of the invention.
Specific embodiment
The present invention is further described in detail with preferred embodiment with reference to the accompanying drawing, referring to Fig. 1-Fig. 5.
1. a kind of construction method of the chaos system of Three Dimensional Generalized dissipation Hamilton system, which is characterized in that including with
Lower step:
(1) Three Dimensional Generalized dissipation Hamilton chaos system (1) are as follows:
X in formula, y, z are state variable；
(2) circuit based on system (1) construction, it is characterised in that: the circuit is made of three channel circuits: first passage
Circuit by multiplier A3, operational amplifier U2C, operational amplifier U2B, operational amplifier U2A and resistance R15, resistance R14,
Resistance R7, resistance R8, resistance R9, resistance R4, resistance R1 and capacitor C1 composition, second channel circuit is by operational amplifier U3C, fortune
Calculate amplifier U3B, operational amplifier U3A and resistance R17, resistance R16, resistance R10, resistance R11, resistance R5, resistance R2 and
Capacitor C2 composition, third channel is by multiplier A2, DC power supply V1, operational amplifier U4C, operational amplifier U4B, operation amplifier
Device U4A and resistance R20, resistance R21, resistance R19, resistance R12, resistance R13, resistance R6, resistance R3 and capacitor C3 composition；The
The output signal feedback of one channel circuit connects resistance R15 as input signal, the output signal are also connected with all the way to input terminal
Multiplier A2 acts on third channel, which is also used as the input signal all the way of multiplier A3 in first passage circuit,
The output signal is also connected with resistance R17 and acts on second channel circuit；The output signal of second channel circuit is fed back to input terminal,
Connection resistance R8 acts on first passage, is also connected with resistance R20 and acts on third channel circuit；The output of third channel circuit is believed
Number feedback arrive input terminal, the output signal connection multiplier A3 act on first passage circuit, the output signal connect resistance R11
Act on second channel circuit；DC power supply V1 connection resistance R13 acts on third channel circuit.
2, multiplier A3 is connected by resistance R9 with the negative input end of operational amplifier U2B in the first passage circuit；
The negative input end of operational amplifier U2C is connected by resistance R14 with the output end of operational amplifier U2C；Operational amplifier U2C's
Positive input terminal ground connection；The output end of operational amplifier U2C is connected by resistance R7 with the negative input end of operational amplifier U2B；Fortune
The negative input end for calculating amplifier U2B is connected by resistance R4 with the output end of operational amplifier U2B；Operational amplifier U2B is just
Input end grounding；The output end of operational amplifier U2B is connected by resistance R1 with the negative input end of operational amplifier U2A；Operation
The negative input end of amplifier U2A is connected by capacitor C1 with the output end of operational amplifier U2A；Operational amplifier U2A's is just defeated
Enter end ground connection, positive power source terminal connection VCC, the negative power end of operational amplifier U2A connects VDD；The output end of operational amplifier U2A
It is connected by resistance R15 with the negative input end of operational amplifier U2C；The output end of operational amplifier U2A passes through resistance R17 and the
The negative input end of operational amplifier U3C in two channel circuits；In the output end connection third channel circuit of operational amplifier U2A
Multiplier A2 two input terminals；The output end of the U2A of operational amplifier connects the multiplier A3's in first passage circuit
One input terminal.
3, the negative input end of the operational amplifier U3C in the second channel circuit passes through resistance R16 and operational amplifier
The output end of U3C is connected；The positive input terminal of operational amplifier U3C is grounded；The output end of operational amplifier U3C passes through resistance R10
It is connected with the negative input end of operational amplifier U3B；The negative input end of operational amplifier U3B passes through resistance R5 and operational amplifier
The output end of U3B is connected；The positive input terminal of operational amplifier U3B is grounded；The output end of operational amplifier U3B by resistance R2 with
The negative input end of operational amplifier U3A is connected；The negative input end of operational amplifier U3A passes through capacitor C2 and operational amplifier U3A
Output end be connected；The positive input terminal of operational amplifier U3A is grounded；The positive supply of operational amplifier U3A terminates VCC, negative supply
Terminate VDD；The output end of operational amplifier U3A is defeated by resistance R8 and bearing for the operational amplifier U2B in first passage circuit
Enter end to be connected；The output end of operational amplifier U3A passes through the negative of the operational amplifier U4C in resistance R20 and third channel circuit
Input terminal is connected.
4, the multiplier A2 in the third channel circuit passes through the negative input end phase of resistance R21 and operational amplifier U4C
Even；The negative input end of operational amplifier U4C is connected by resistance R19 with the output end of operational amplifier U4C；Operational amplifier
The positive input terminal of U4C is grounded；The output end of operational amplifier U4C passes through the negative input end phase of resistance R12 and operational amplifier U4B
Even；The negative input end of operational amplifier U4B is connected by resistance R6 with the output end of operational amplifier U4B；Operational amplifier U4B
Positive input terminal ground connection；The output end of operational amplifier U4B is connected by resistance R3 with the negative input end of operational amplifier U4A；
The negative input end of operational amplifier U4A is connected by capacitor C3 with the output end of operational amplifier U4A；Operational amplifier U4A's
Positive input terminal ground connection；Positive supply termination VCC, the negative supply of operational amplifier U4A terminates VDD；The output end of operational amplifier U4A
Connect the other end of the multiplier A3 in first passage circuit；The output end of operational amplifier U4A is logical by resistance R11 and second
The negative input end of operational amplifier U3B in road circuit is connected；One end of DC power supply V1 is grounded；The other end of DC power supply V1
Pass through the negative input end of resistance R13 and operational amplifier U4B.
Certainly, above description is not limitation to invention, and the present invention is also not limited to the example above, the art it is general
The variations, modifications, additions or substitutions that logical technical staff is made within the essential scope of the present invention also belong to protection of the invention
Range.
Claims (1)
1. a kind of chaos circuit of Three Dimensional Generalized dissipation Hamilton system, it is characterised in that: the circuit is by three channel circuits
Composition: first passage circuit is by multiplier A3, operational amplifier U2C, operational amplifier U2B, operational amplifier U2A and resistance
R15, resistance R14, resistance R7, resistance R8, resistance R9, resistance R4, resistance R1 and capacitor C1 composition, second channel circuit is by operation
Amplifier U3C, operational amplifier U3B, operational amplifier U3A and resistance R17, resistance R16, resistance R10, resistance R11, resistance
R5, resistance R2 and capacitor C2 composition, third channel is by multiplier A2, DC power supply V1, operational amplifier U4C, operational amplifier
U4B, operational amplifier U4A and resistance R20, resistance R21, resistance R19, resistance R12, resistance R13, resistance R6, resistance R3 and
Capacitor C3 composition；The output signal feedback of first passage circuit connects resistance R15 as input signal all the way, is somebody's turn to do to input terminal
Output signal is also connected with multiplier A2 and acts on third channel, which is also used as multiplier A3 in first passage circuit
Input signal all the way, the output signal are also connected with resistance R17 and act on second channel circuit；The output signal of second channel circuit
Input terminal is fed back, connection resistance R8 acts on first passage, is also connected with resistance R20 and acts on third channel circuit；Third is logical
The output signal feedback of road circuit is to input terminal, and output signal connection multiplier A3 acts on first passage circuit, the output
Signal connection resistance R11 acts on second channel circuit；DC power supply V1 connection resistance R13 acts on third channel circuit；
Multiplier A3 is connected by resistance R9 with the negative input end of operational amplifier U2B in the first passage circuit；Operation is put
The negative input end of big device U2C is connected by resistance R14 with the output end of operational amplifier U2C；The positive input of operational amplifier U2C
End ground connection；The output end of operational amplifier U2C is connected by resistance R7 with the negative input end of operational amplifier U2B；Operation amplifier
The negative input end of device U2B is connected by resistance R4 with the output end of operational amplifier U2B；The positive input terminal of operational amplifier U2B
Ground connection；The output end of operational amplifier U2B is connected by resistance R1 with the negative input end of operational amplifier U2A；Operational amplifier
The negative input end of U2A is connected by capacitor C1 with the output end of operational amplifier U2A；The positive input of operational amplifier U2A terminates
Ground, positive power source terminal connection VCC, the negative power end of operational amplifier U2A connect VDD；The output end of operational amplifier U2A passes through electricity
Resistance R15 is connected with the negative input end of operational amplifier U2C；The output end of operational amplifier U2A passes through resistance R17 and second channel
The negative input end of operational amplifier U3C in circuit；Multiplication in the output end connection third channel circuit of operational amplifier U2A
Two input terminals of device A2；One of multiplier A3 in the output end connection first passage circuit of the U2A of operational amplifier is defeated
Enter end；
The negative input end of operational amplifier U3C in the second channel circuit is defeated by resistance R16 and operational amplifier U3C's
Outlet is connected；The positive input terminal of operational amplifier U3C is grounded；The output end of operational amplifier U3C is put by resistance R10 with operation
The negative input end of big device U3B is connected；The negative input end of operational amplifier U3B passes through the output of resistance R5 and operational amplifier U3B
End is connected；The positive input terminal of operational amplifier U3B is grounded；The output end of operational amplifier U3B passes through resistance R2 and operation amplifier
The negative input end of device U3A is connected；The negative input end of operational amplifier U3A passes through the output end of capacitor C2 and operational amplifier U3A
It is connected；The positive input terminal of operational amplifier U3A is grounded；Positive supply termination VCC, the negative supply of operational amplifier U3A terminates VDD；
The output end of operational amplifier U3A is connected by resistance R8 with the negative input end of the operational amplifier U2B in first passage circuit；
The output end of operational amplifier U3A passes through the negative input end phase of resistance R20 and the operational amplifier U4C in third channel circuit
Even；
Multiplier A2 in the third channel circuit is connected by resistance R21 with the negative input end of operational amplifier U4C；Operation
The negative input end of amplifier U4C is connected by resistance R19 with the output end of operational amplifier U4C；Operational amplifier U4C's is just defeated
Enter end ground connection；The output end of operational amplifier U4C is connected by resistance R12 with the negative input end of operational amplifier U4B；Operation is put
The negative input end of big device U4B is connected by resistance R6 with the output end of operational amplifier U4B；The positive input of operational amplifier U4B
End ground connection；The output end of operational amplifier U4B is connected by resistance R3 with the negative input end of operational amplifier U4A；Operation amplifier
The negative input end of device U4A is connected by capacitor C3 with the output end of operational amplifier U4A；The positive input terminal of operational amplifier U4A
Ground connection；Positive supply termination VCC, the negative supply of operational amplifier U4A terminates VDD；The output end connection first of operational amplifier U4A
The other end of multiplier A3 in channel circuit；The output end of operational amplifier U4A passes through in resistance R11 and second channel circuit
Operational amplifier U3B negative input end be connected；One end of DC power supply V1 is grounded；The other end of DC power supply V1 passes through resistance
The negative input end of R13 and operational amplifier U4B.
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| CN112152773B (en) * | 2019-06-28 | 2022-08-02 | 天津科技大学 | Three-dimensional improved Sprott-A chaotic system and circuit implementation thereof |
| CN112152983B (en) * | 2019-06-28 | 2022-05-20 | 天津科技大学 | non-Hamilton system with six clusters of chaotic streams and construction method thereof |
| CN112152774B (en) * | 2019-06-28 | 2022-08-02 | 天津科技大学 | Construction method of non-Hamilton system capable of generating four-scroll chaotic stream |
| CN112152772B (en) * | 2019-06-28 | 2022-08-02 | 天津科技大学 | Conservative system with double-cluster chaotic streams and circuit implementation thereof |
| CN112422766B (en) * | 2019-08-23 | 2022-07-29 | 天津科技大学 | Generalized Sprott-A system with three-dimensional 2 x 1 cluster conservative chaotic stream and circuit implementation thereof |
| CN112422260B (en) * | 2019-08-23 | 2022-08-02 | 天津科技大学 | Construction method of non-Hamilton system with three-dimensional 2 x 2 cluster conservative chaotic stream |
| 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 |
| CN111835498B (en) * | 2020-06-24 | 2024-03-29 | 佛山科学技术学院 | Multi-wing chaotic signal generator and encryption system |
| CN113078995A (en) * | 2021-04-23 | 2021-07-06 | 上海理工大学 | High-complexity four-dimensional hyperchaotic circuit |
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