CN106817213B - A kind of fractional order nonlinear chaos system circuit - Google Patents
A kind of fractional order nonlinear chaos system circuit Download PDFInfo
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- CN106817213B CN106817213B CN201510848949.1A CN201510848949A CN106817213B CN 106817213 B CN106817213 B CN 106817213B CN 201510848949 A CN201510848949 A CN 201510848949A CN 106817213 B CN106817213 B CN 106817213B
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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 invention discloses a kind of discontinuous chaos system circuits of novel fractional order with absolute value term, including first passage circuit, second channel circuit and third channel circuit, there are two one output ends of input terminal for first passage circuit, there are three two output ends of input terminal for second channel circuit, third channel circuit has an input terminal, an output end；The input terminal of three channel circuits interconnects with output end, constitutes fractional order nonlinear chaos system circuit, the output end of first passage circuitInput terminal as second channel circuit, the output end of second channel circuit is as the input terminal of first passage circuit and the input terminal of third channel circuit, input terminal of the output end of second channel circuit as second channel circuit, the output end of third channel circuit is as the input terminal of the first circuit passband and the input terminal of second channel circuit.The discontinuous chaos system, construction is convenient, and chaos state is stablized, it is easy to accomplish, in engineering field with good application prospect.
Description
Technical field
The invention belongs to field of information encryption, especially a kind of fractional order nonlinear chaos system circuit.
Background technique
Nonlinear science is referred to as " the third time revolution " of scientific circles.Nonlinear science and the every field of people's life are all
Closely bound up, and gradually changed the world outlook of people, it allows people's thinking to become active, consider a problem more comprehensively,
Rationality.Scholars generally believe: non-linear mainly to consist of three parts, they are therefore chaos, point shape and orphan mix respectively
Ignorant theory is held the balance in non-linear subject.Research chaos system has huge potential value to the progress of science and technology.
Chaos is a kind of determining sexual behaviour that a determining Kind of Nonlinear Dynamical System is showed, and is regular
The performance of irregular movement in system.Professor Lorenz in 1963 has found first chaos system and is named as Lorenz and mixes
Ignorant system.The it is proposed of the system means the origin of Chaos, becomes a hot topic of scientists study from this chaotic motion
Field.The research of chaos system is developing with rapid changepl. never-ending changes and improvementsly, and scholars have found more and more new type of chaotic system, these
The it is proposed of new system promotes the development of chaology.For example, R ssler system, Chua ' s circuit, Chen system, L ü chaos
System.In recent years, researcher constantly explores new fractional-order system, and more and more new fractional-order systems are constantly suggested, and such as divides
Number rank Chua ' s circuits, fractional order R ssler chaos system, fractional order Lorenz chaos system, fractional order unified system,
Fractional order L ü chaos system etc..
With the discovery of chaos system, the research of Chaotic Synchronous gradually becomes the heat subject of researcher, people also by
Gradually propose more and more feasible, methods of synchronously control for using.Chaotic Synchronous is applied to the every field of life,
Such as secret communication, therapeutic treatment, bioengineering.
Currently, most researchs are realized based on computer emulation method, system model is carried out frequently with Matlab simulation software
It is emulated with control method, circuit structure emulation is carried out using Multisim simulation software.But numerical simulation and actual circuit structure
It makes that there are still certain othernesses, is especially limited by the physical characteristic of actual components, the chaos circuit of theory deduction is not
Centainly can successfully it reappear in actual circuit.
Summary of the invention
The purpose of the present invention is to provide a kind of fractional order nonlinear chaos system circuits.
The technical solution for realizing the aim of the invention is as follows: a kind of fractional order nonlinear chaos system circuit, including first
Channel circuit, second channel circuit and third channel circuit, first passage circuit is there are two input terminal, respectively y and z', and one
Output end is x, and second channel circuit is there are three input terminal, respectively y', z' and x, two output ends, respectively y and y', third
It is y that channel circuit, which has an input terminal, and an output end is z'；The input terminal of three channel circuits is interconnected on output end
Together, fractional order nonlinear chaos system circuit, input of the output end x of first passage circuit as second channel circuit are constituted
Holding x, the output end y of second channel circuit is as the input terminal y of first passage circuit and the input terminal y of third channel circuit, and the
Input terminal y' of the output end y' of two channel circuits as second channel circuit, the output end z' of third channel circuit is as first
The input terminal z' of the circuit passband and input terminal z' of second channel circuit；
The equivalent mathematical model of the circuit are as follows:
In formula, m1> 0.89, m2> 0.8, m3> 0.91, k > 0, x, y, z are the signal in nonlinear chaotic system circuit,For the m of x1Order derivative,For the m of y2Order derivative,For the m of z3Order derivative.
The present invention is compared with existing chaos system and building method, remarkable advantage are as follows: 1) chaos system proposed by the present invention
System has fractional order chaotic characteristic, is more suitable for applying in secret communication field；2) chaos system proposed by the present invention is using exhausted
To value item instead of the quadratic term in original system, third channel voltage magnitude is obviously reduced, and is conducive to the realization of circuit system；3)
The increase of absolute value term of the invention can pass through so that the output voltage amplitude of novel circuit first passage and second channel is adjustable
Adjustable resistance flexible setting provides convenience for circuit application；4) circuit system can guarantee system in amplitude adjustment process
Lyapunov index it is constant, thus the chaotic characteristic of circuit remains unchanged, and is conducive to systematic difference；5) present invention uses office
Portion's range of decrease method improves the design method of chaos hardware circuit, good with the consistency of numerical simulation, and circuit structure is convenient, chaos shape
State is stablized, it is easy to accomplish, in engineering field with good application prospect.
Detailed description of the invention
Fig. 1 is fractional order nonlinear chaos system circuit entire block diagram of the invention.
Fig. 2 is the coexisting attractors of novel chaotic systems with fractional order proposed by the present invention.
Fig. 3 is the circuit diagram of novel chaotic systems with fractional order first passage proposed by the present invention.
Fig. 4 is the circuit diagram of novel chaotic systems with fractional order second channel proposed by the present invention.
Fig. 5 is the circuit diagram of novel chaotic systems with fractional order third channel proposed by the present invention.
Fig. 6 is the Lyapunov index curve diagram of chaotic systems with fractional order proposed by the present invention.
Specific embodiment
In conjunction with Fig. 1, a kind of fractional order nonlinear chaos system circuit of the invention, including it is first passage circuit, second logical
Road circuit and third channel circuit, for first passage circuit there are two input terminal, respectively y and z', an output end is x, second
There are three input terminals, respectively y', z' and x for channel circuit, and two output ends, respectively y and y', third channel circuit have one
Input terminal is y, and an output end is z'；The input terminal of three channel circuits interconnects with output end, constitutes score
Rank nonlinear chaotic system circuit, input terminal x of the output end x of first passage circuit as second channel circuit, second channel
The output end y of circuit as the input terminal y of first passage circuit and the input terminal y of third channel circuit, second channel circuit
The input of output end y' the input terminal y' as second channel circuit, the output end z' of third channel circuit as the first circuit passband
Hold the input terminal z' of z' and second channel circuit；
The equivalent mathematical model of the circuit are as follows:
In formula, m1> 0.89, m2> 0.8, m3> 0.91, k > 0, x, y, z are the signal in nonlinear chaotic system circuit,For the m of x1Order derivative,For the m of y2Order derivative,For the m of z3Order derivative.
In conjunction with Fig. 3, the first passage circuit includes first resistor R1, second resistance R2,3rd resistor R3, the 4th resistance
R4, the 5th resistance R5, the 6th resistance R6, the 7th resistance R7, the 8th resistance R8, the 9th resistance R9, the tenth resistance R10, the 11st
Resistance R11, twelfth resistor R12, thirteenth resistor R13, the 14th resistance R14, the 15th resistance R15, the 16th resistance
R16, the 17th resistance R17, the 18th resistance R18, the 19th resistance 19, first capacitor C1, the second capacitor C2, third capacitor
C3, the 4th capacitor C4, the 5th capacitor C5, the first multiplier A1, the second multiplier A2, the first operational amplifier U1A, the second operation
Amplifier U2A, third operational amplifier U3A, four-operational amplifier U4A and the 5th operational amplifier U5A；Wherein the first multiplication
Two input terminals of device A1 are the input terminal y and input terminal z' of first passage circuit, the input terminal z' of first passage circuit and the
An input terminal of paired multiplier A2 connects, and another input terminal of the output end of the first multiplier A1 and the second multiplier A2 connect
It connects, the output end of the second multiplier A2 is connect with one end of first resistor R1, and the other end of first resistor R1 is put with the first operation
The negative input end connection of big device U1A, the positive input terminal of the first operational amplifier U1A are connected to ground, the other end of first resistor R1
It being connect simultaneously with one end of second resistance R2, the other end of second resistance R2 is connect with the output end of the first operational amplifier U1A,
The other end of second resistance R2 is connect with one end of 3rd resistor R3 simultaneously, the other end of 3rd resistor R3 and the 4th resistance R4's
The other end of one end connection, 3rd resistor R3 is connect with the negative input end of second operational amplifier U2A simultaneously, the second operation amplifier
The positive input terminal of device U2A is connected to ground, and the other end of the 4th resistance R4 is connect with the output end of second operational amplifier U2A, the
The other end of four resistance R4 is connect with one end of the 5th resistance R5 simultaneously, and the one of the other end of the 5th resistance R5 and the 6th resistance R6
End connection, the other end of the 5th resistance R5 connects with one end of the 8th resistance R8 simultaneously, the other end of the 5th resistance R5 and meanwhile with
One end of first capacitor C1 connects, and the other end of the 5th resistance R5 is connect with one end of the second capacitor C2 simultaneously, the 5th resistance R5
The other end connect simultaneously with one end of the 4th capacitor C4, the other end of the 5th resistance R5 simultaneously with one end of the 5th capacitor C5 company
It connects, the other end of the 5th resistance R5 is connect with the negative input end of third operational amplifier U3A simultaneously, third operational amplifier U3A
Positive input terminal be connected to ground, the other end of the 6th resistance R6 is connect with one end of the 7th resistance R7, and the 8th resistance R8's is another
End is connect with one end of the 9th resistance R9, and the other end of the 9th resistance R9 is connect with one end of the tenth resistance R10, the tenth resistance
The other end of R10 is connect with one end of eleventh resistor R11, the other end of eleventh resistor R11 and the one of twelfth resistor R12
End connection, the other end of twelfth resistor R12 are connect with one end of thirteenth resistor R13, and the other end of twelfth resistor R12 is same
When connect with the other end of first capacitor C1, the other end of thirteenth resistor R13 is connect with one end of the 14th resistance R14,
The other end of 14 resistance R14 is connect with one end of the 15th resistance R15, and the other end of the second capacitor C2 is with third capacitor C3's
The other end of one end connection, the 14th resistance R14 is connect with the other end of third capacitor C3 simultaneously, the other end of the 4th capacitor C4
It is connect with the other end of the 5th capacitor C5, the other end of the 7th resistance R7 is connect with the other end of the 15th resistance R15, the 7th electricity
The other end for hindering R7 is connect with the other end of the 4th capacitor C4 simultaneously, and the other end of the 7th resistance R7 is simultaneously with the 5th capacitor C5's
The other end of other end connection, the 7th resistance R7 is connect with the output end of third operational amplifier U3A simultaneously, the 7th resistance R7's
The other end is connect with one end of the 16th resistance R16 simultaneously, and the one of the other end of the 16th resistance R16 and the 17th resistance R17
The other end of end connection, the 16th resistance R16 is connect with the negative input end of four-operational amplifier U4A simultaneously, and the 4th operation is put
The positive input terminal of big device U4A is connected to ground, and the other end of the 17th resistance R17 and the output end of four-operational amplifier U4A connect
Connect, the output end of four-operational amplifier U4A is connect with one end of the 18th resistance R18, the other end of the 18th resistance R18 with
One end of 19th resistance R19 connects, and the other end of the 18th resistance R18 and the negative input end of the 5th operational amplifier U5A connect
It connects, the positive input terminal of the 5th operational amplifier U5A is connected to ground, the other end and the 5th operational amplifier of the 19th resistance R19
The output end of U5A connects, output end x of the output end of the 5th operational amplifier U5A as first passage circuit.
In conjunction with Fig. 4, the second channel circuit includes the 20th resistance R20, the 21st resistance R21, the 22nd electricity
Hinder R22, the 23rd resistance R23, the 24th resistance R24, the 25th resistance R25, the 26th resistance R26, the 20th
Seven R27, the 28th resistance R28, the 29th resistance R29, the 30th resistance R30, the 31st resistance R31, the 32nd
Resistance R32, the 33rd resistance R33, the 34th resistance R34, the 35th resistance R35, the 36th resistance R36, third
17 resistance R37, the 6th capacitor C6, the 7th capacitor C7, the 8th capacitor C8, the 9th capacitor C9, the tenth capacitor C10, the 11st electricity
Hold C11, the 12nd capacitor C12, the 13rd capacitor C13, the 14th capacitor C14, the 15th capacitor C15, third multiplier A3, the
Six operational amplifier U6A, the 7th operational amplifier U7A, the 8th operational amplifier U8A, the fortune of the 9th operational amplifier U9A and the tenth
Calculate amplifier U10A；One end of 20th resistance R20 is the input terminal y' of second channel circuit, and the 20th resistance R20's is another
End is connect with one end of the 21st resistance R21, and the other end of the 20th resistance R20 is simultaneously with the 6th operational amplifier U6A's
Negative input end connection, the positive input terminal of the 6th operational amplifier U6A is connected to ground, the other end of the 21st resistance R21 and the
The output end of six operational amplifier U6A connects, the other end of the 21st resistance R21 simultaneously with the 22nd resistance R22 one
End connection, the other end of the 22nd resistance R22 are connect with one end of the 23rd resistance R23, and two of third multiplier A3
Input terminal is respectively the input terminal z' and input terminal x of second channel circuit, the output end of third multiplier A3 and the 24th electricity
One end connection of R24 is hindered, the other end of the 24th resistance R24 is connect with the negative input end of the 7th operational amplifier U7A, and the 7th
The positive input terminal of operational amplifier U7A is connected to ground, the other end of the 24th resistance R24 simultaneously with the 25th resistance R25
One end connection, the other end of the 25th resistance R25 connect with the output end of the 7th operational amplifier U7A, and the 25th is electric
The other end for hindering R25 is connect with one end of the 26th resistance R26 simultaneously, the other end and the 20th of the 26th resistance R26
The other end of three resistance R23 connects, and the other end of the 26th resistance R26 is connect with one end of the 27th resistance R27 simultaneously,
The other end of 27th resistance R27 is connect with one end of the 28th resistance R28, the other end of the 28th resistance R28 with
One end of 29th resistance R29 connects, and the other end of the 29th resistance R29 is connect with one end of the 30th resistance R30, the
The other end of 30 resistance R30 is connect with one end of the 31st resistance R31, the other end and third of the 31st resistance R31
One end of 12 resistance R32 connects, and the other end of the 32nd resistance R32 is connect with one end of the 33rd resistance R33, and second
The other end of 16 resistance R26 is connect with one end of the 6th capacitor C6 simultaneously, the other end of the 6th capacitor C6 and the 29th electricity
The other end connection of R29 is hindered, the other end of the 26th resistance R26 is connect with one end of the 7th capacitor C7 simultaneously, the 7th capacitor
The other end of C7 is connect with the other end of the 29th resistance R29, the other end of the 26th resistance R26 simultaneously with the 8th capacitor
One end of C8 connects, and the other end of the 8th capacitor C8 is connect with the other end of the 29th resistance R29, the 26th resistance R26
The other end connect simultaneously with one end of the 9th capacitor C9, the other end of the 9th capacitor C9 is another with the 29th resistance R29's
The other end of end connection, the 26th resistance R26 is connect with one end of the tenth capacitor C10 simultaneously, the other end of the tenth capacitor C10
Connect with the other end of the 31st resistance R31, the other end of the 26th resistance R26 simultaneously with the 11st capacitor C11 one
End connection, the other end of the 11st capacitor C11 are connect with the other end of the 31st resistance R31, and the 26th resistance R26's is another
One end is connect with one end of the 12nd capacitor R12 simultaneously, and the other end of the 12nd capacitor R12 is another with the 31st resistance R31's
The other end of one end connection, the 26th resistance R26 is connect with one end of the 13rd capacitor C13 simultaneously, the 13rd capacitor C13's
The other end is connect with the other end of the 33rd resistance R33, the other end of the 26th resistance R26 simultaneously with the 14th capacitor
One end of C14 connects, and the other end of the 14th capacitor C14 is connect with the other end of the 33rd resistance R33, the 26th resistance
The other end of R26 is connect with one end of the 15th capacitor C15 simultaneously, the other end and the 33rd resistance of the 15th capacitor C15
The other end of R33 connects, and the other end of the 26th resistance R26 is connect with the negative input end of the 8th operational amplifier U8A simultaneously,
The positive input terminal of 8th operational amplifier U8A is connected to ground, the output end and the 33rd resistance of the 8th operational amplifier U8A
The other end of R33 connects, output end y' of the output end of the 8th operational amplifier U8A as second channel circuit, second channel
The output end y' of circuit is connect with one end of the 34th resistance R34 simultaneously, the other end and the 30th of the 34th resistance R34
One end of five resistance R35 connects, the other end of the 34th resistance R34 while the negative input end with the 9th operational amplifier U9A
Connection, the positive input terminal of the 9th operational amplifier U9A are connected to ground, and the other end and the 9th operation of the 35th resistance R35 is put
The output end connection of big device U9A, the other end of the 35th resistance R35 are connect with one end of the 36th resistance R36 simultaneously, the
The other end of 36 resistance R36 is connect with one end of the 37th resistance R37, and the other end of the 36th resistance R36 is simultaneously
It is connect with the negative input end of the tenth operational amplifier U10A, the positive input terminal of the tenth operational amplifier U10A is connected to ground, third
The other end of 17 resistance R37 is connect with the output end of the tenth operational amplifier U10A, and the tenth operational amplifier U10A's is defeated
Output end y of the outlet as second channel circuit.
In conjunction with Fig. 5, the third channel circuit includes slide rheostat R38, the 38th resistance R39, the 39th electricity
Hinder R40, the 40th resistance R41, the 41st resistance R42, the 42nd resistance R43, the 43rd resistance R44, the 44th
Resistance R45, the 45th resistance R46, the 46th resistance R47, the 47th resistance R48, the 48th resistance R49, the 4th
19 resistance R50, the 50th resistance R51, the 51st resistance R52, the 52nd resistance R53, the 16th capacitor C16, the tenth
Seven capacitor C17, the 18th capacitor C18, the 19th capacitor C19, the 20th capacitor C20, the 21st capacitor C21, the one or two pole
Pipe D1, the second diode D2, the 11st operational amplifier U11A, the 12nd operational amplifier U12A, the 13rd operational amplifier
U13A and the tenth four-operational amplifier U14A；Input terminal of the fixing end of slide rheostat R38 as third channel circuit
The sliding end of y, slide rheostat R38 are connect with the anode of first diode D1, the negative terminal of first diode D1 and the 11st fortune
The negative input end connection of amplifier U11A is calculated, the positive input terminal of the 11st operational amplifier U11A is connected to ground, first diode
The negative terminal of D1 connect with one end of the 38th resistance R39 simultaneously, the anode of first diode D1 and meanwhile with the second diode
The negative terminal of D2 connects, and the other end of the 38th resistance R39 is connect with the output end of the 11st operational amplifier U11A, and the 30th
The other end of eight resistance R39 is connect with one end of the 39th resistance R40 simultaneously, the other end of the 39th resistance R40 and the
The anode of two diode D2 connects, and the other end of the 39th resistance R40 is connect with one end of the 40th resistance R41 simultaneously, the
The other end of 39 resistance R40 is connect with one end of the 41st resistance R42 simultaneously, the other end of the 41st resistance R42
It is connect with one end of the 42nd resistance R43, the other end of the 42nd resistance R43 and one end of the 43rd resistance R44 connect
It connects, the other end of the 43rd resistance R44 is connect with one end of the 44th resistance R45, the other end of the 44th resistance R45
It is connect with one end of the 45th resistance R46, the other end of the 45th resistance R46 and one end of the 46th resistance R47 connect
It connects, the other end of the 46th resistance R47 is connect with one end of the 47th resistance R48, the other end of the 47th resistance R48
It is connect with one end of the 48th resistance R49, the other end of the 39th resistance R40 while one end with the 16th capacitor C16
Connection, the other end of the 16th capacitor C16 connect with one end of the 17th capacitor C17, the other end of the 17th capacitor C17 and the
The other end of 45 resistance R46 connects, and the other end of the 39th resistance R40 connects with one end of the 18th capacitor C18 simultaneously
It connects, the other end of the 18th capacitor C18 is connect with one end of the 19th capacitor C19, the other end and the 4th of the 19th capacitor C19
The other end of 17 resistance R48 connects, and the other end of the 39th resistance R40 is connect with one end of the 20th capacitor C20 simultaneously,
The other end of 20th capacitor C20 is connect with the other end of the 48th resistance R49, and the other end of the 39th resistance R40 is same
One end of 21 capacitor C21 of Shi Yu connects, and the other end of the 21st capacitor C21 is another with the 48th resistance R49's
The other end of end connection, the 39th resistance R40 is connect with the negative input end of the 12nd operational amplifier U12A simultaneously, and the 12nd
The positive input terminal of operational amplifier U12A is connected to ground, the output end and the 48th resistance of the 12nd operational amplifier U12A
The other end of R49 connects, and the other end of the 40th resistance R41 is connect with the other end of the 48th resistance R49,40 resistance
The other end of R41 is connect with one end of the 49th resistance R50 simultaneously, the other end of the 49th resistance R50 and the 50th electricity
One end connection of R51 is hindered, the other end of the 49th resistance R50 connects with the negative input end of the 13rd operational amplifier U13A simultaneously
It connects, the positive input terminal of the 13rd operational amplifier U13A is connected to ground, and the other end and the 13rd operation of 50 resistance R51 is put
The output end connection of big device U13A, the output end of the 13rd operational amplifier U13A while one end with the 51st resistance R52
Connection, the other end of the 51st resistance R52 are connect with one end of the 52nd resistance R53, and the 51st resistance R52's is another
End is connect with the negative input end of the tenth four-operational amplifier U14A simultaneously, the positive input terminal and ground of the tenth four-operational amplifier U14A
Connection, output end z' of the other end of the 52nd resistance R53 as third channel circuit.
The model of above-mentioned all operational amplifiers is all the same, and power supply is ± 15V DC power supply.
The first resistor R1,3rd resistor R3, the 16th resistance R16, the 17th resistance R17, the 18th resistance R18,
20th resistance R20, the 21st resistance R21, the 24th resistance R24, the 34th resistance R34, the 35th resistance
R35, the 36th resistance R36, the 38th resistance R39, the 39th resistance R40, the 49th resistance R50, the 50th electricity
Hindering R51 and the 52nd resistance R53 is 10k Ω, second resistance R2, the 4th resistance R4, the 25th resistance R25, the 20th
Six resistance R26 and the 40th resistance R41 are 100k Ω, and the 5th resistance R5 is 500k Ω, and the 6th resistance R6 is 30k Ω, and the 7th
Resistance 7 is 5.6k Ω, the 8th resistance R8, the 9th resistance R9, the tenth resistance R10, the 27th resistance R27, the 28th resistance
R28, the 41st resistance R42, the 42nd resistance R43 and the 43rd resistance R44 are 22M Ω, and eleventh resistor R11 is
15M Ω, twelfth resistor R12 be 931k Ω, thirteenth resistor R13 be 1.2M Ω, the 14th resistance R14 be 20k Ω, the 15th
Resistance R15 is 3.9k Ω, and the 19th resistance R19 is 250k Ω, and the 22nd resistance R22 is 82k Ω, the 23rd resistance R23
It is 681k Ω for 1.3k Ω, the 29th resistance R29, the 30th resistance R30 is 5.1M Ω, and the 31st resistance R31 is 78.8k
Ω, the 32nd resistance R32 are 240k Ω, and the 33rd resistance R33 is 11k Ω, the electricity of the 37th resistance R37 and the 51st
Resistance R52 is 50k Ω, and the 44th resistance R45 is 9.1M Ω, and the 45th resistance R46 is 732k Ω, the 46th resistance
R47 is 3.3M Ω, and the 47th resistance R48 is 261k Ω, and the 48th resistance R49 is 36.5k Ω, slide rheostat R38's
Maximum value is 200k Ω, first capacitor C1, the 4th capacitor C4, the 15th capacitor C15, the 18th capacitor C18, the 20th capacitor
C20 is 0.22uF, and the second capacitor C2 and the 16th capacitor C16 are 0.33uF, third capacitor C3, the 5th capacitor C5 and second
11 capacitor C21 are 0.47uF, and the 6th capacitor C6 and the tenth capacitor C10 are 0.1uF, the 7th capacitor C7, the 8th capacitor C8,
11st capacitor C11, the 12nd capacitor C12, the 13rd capacitor C13 and the 14th capacitor C14 are 0.15uF, the 9th capacitor C9
For 0.3uF, the 17th capacitor C17 and the 19th capacitor C19 are 1uF.
The discontinuous chaos system of novel fractional order of the invention and its circuit structure are carried out below in conjunction with Detailed description of the invention detailed
Thin description.
A kind of discontinuous chaos system of novel fractional order and its circuit structure construction method, specifically:
Step 1, the overall model for proposing the novel discontinuous three-dimensional chaotic system of integer rank.
1) model of the continuous three-dimensional chaotic system of former integer rank are as follows:
2) improved model of the discontinuous chaos system of new fractional order are as follows:
In formula, m1>0.89,m2>0.8,m3> 0.91, k value can be changed (k > 0).The coexisting attractors of novel system are shown in Fig. 2.
The overall structure of step 2, the novel discontinuous chaos circuit of design, is made of three channel circuits:
1) first passage is made of multiplier A1, A2, operational amplifier U1A, U2A, U3A, U4A, U5A and resistance, capacitor.
2) second channel is made of multiplier A3, operational amplifier U6A, U7A, U8A, U9A, U10A and resistance, capacitor.
3) third channel is made of diode D1, D2, operational amplifier U11A, U12A, U13A, U14A and resistance, capacitor.
4) final output signal of whole system is x, y, z, and in order to which signal is effectively transmitted and exported, intermediate node signal is
x'、y'、z'。
Step 3, design first passage circuit structure, first passage final output signal are x.First passage is by multiplier
A1, A2, operational amplifier U1A, U2A, U3A, U4A, U5A and resistance capacitance are constituted, as shown in Figure 3.First passage circuit is specific
It constitutes as follows:
1) second channel output valve y and third channel output signal z' are input to multiplier A1, and A1 output signal and z' are defeated
Enter to multiplier A2, obtains output signal a=0.01yz'2。
2) since two-stage multiplier makes output signal reduce 100 times, it is therefore desirable to amplify output signal a.Signal a warp
Two-stage calculation amplifier circuit amplifies 100 times, obtains output signal b=yz'2, wherein first order amplifying circuit is by resistance R1 (10k
Ω), R2 (100k Ω) and operational amplifier U1A are constituted, second level amplifying circuit by resistance R3 (10k Ω), R4 (100k Ω) and
Operational amplifier U2A is constituted.
3) signal b is through resistance R5 (500k Ω), R6 (30k Ω), R7 (5.6k Ω), fractional order circuit and operational amplifier
U3A output, to obtainI.e.
4) fractional order circuit is made of a series of resistance capacitances.In the circuit that the present invention announces, first passage is with m1=
For 0.96, by R8 (22M Ω), R9 (22M Ω), R10 (22M Ω), R11 (15M Ω), R12 (931k Ω), R13 (1.2M Ω),
R14 (20k Ω), R15 (3.9k Ω), capacitor C1 (0.22uF), C2 (0.33uF), C3 (0.47uF), C4 (0.22uF), C5
(0.47uF) is constituted.
5) signal x' obtains first passage output signal x=25x', i.e., after dual-stage amplifier circuit amplifies 25 timesFirst order amplifying circuit is by resistance R16 (10k Ω), R16 (10k Ω) and operational amplifier U4A
It constitutes, second level amplifying circuit is made of resistance R18 (10k Ω), R19 (250k Ω) and operational amplifier U5A.
6) it may be noted that in third channel construction process, z=5z', thenRealize the function of first passage in system model.
Step 4, design second channel circuit structure, second channel final output signal are y and y'.Second channel is by multiplication
Device A3, operational amplifier U6A, U7A, U8A, U9A, U10A and resistance, capacitor are constituted, as shown in Figure 4.Second channel circuit is specific
It constitutes as follows:
1) signal y' is exported through R20 (10k Ω), R21 (10k Ω) and operational amplifier U6A, obtains signal c=-y'.
2) signal z' and first passage signal x are input to multiplier A3, obtain d=0.1xz'.
3) signal d is exported through R24 (10k Ω), R25 (100k Ω) and operational amplifier U7A, obtains signal e=-xz'.
4) for signal c through R22 (82k Ω), R23 (1.3k Ω), signal e is common to input fractional order electricity after R22 (82k Ω)
Road and operational amplifier U8A, to be
5) fractional order circuit is made of a series of resistance capacitances.In the circuit that the present invention announces, second channel is with m2=
For 0.85, by R27 (22M Ω), R28 (22M Ω), R29 (681k Ω), R30 (5.1M Ω), R31 (78.7k Ω), R32
(240k Ω), R33 (11k Ω), capacitor C6 (0.1uF), C7 (0.15uF), C8 (0.15uF), C9 (0.32uF), C10
(0.1uF), C11 (0.15uF), C12 (0.15uF), C13 (0.15uF), C14 (0.15uF) and C15 (0.22uF) are constituted.
6) signal y' obtains output signal y=5y', i.e., after second amplifying circuit amplifies 5 timesWherein first order amplifying circuit is by resistance R34 (10k Ω), R35 (10k Ω) and operational amplifier
U9A is constituted, and second level amplifying circuit is made of resistance R36 (10k Ω), R37 (50k Ω) and operational amplifier U10A.
7) it may be noted that in third channel construction process, z=5z', thenRealization system mould
The function of second channel in type.
Step 5, design third channel circuit structure, second channel final output signal are z.Third channel is by diode
D1, D2, operational amplifier U11A, U12A, U13A, U14A and resistance capacitance are constituted, as shown in Figure 5.Third channel circuit is specific
It constitutes as follows:
1) second channel output signal y is through slide rheostat R38 (0-200k Ω), diode D1 (D1N4148), D2
(D1N4148), resistance R39 (10k Ω), R40 (10k Ω) and operational amplifier U11A export f=k | y |, wherein diode D1,
D2 and operational amplifier U11A main composition absolute value circuit, slide rheostat R38 constitute the function of model adjustable parameter k.With k
For=8, R38 resistance value is adjusted to 125k Ω.
2) signal f constitutes integrating circuit through resistance fractional order circuit and operational amplifier U12A, obtains third channel output
SignalI.e.Realize the function of third channel in system model.
3) fractional order circuit is (with m3For=0.95) by R41 (100k Ω), R42 (22M Ω), R43 (22M Ω), R44
(22M Ω), R45 (9.1M Ω), R46 (732k Ω), R47 (3.3M Ω), R48 (261k Ω), R49 (36.5k Ω), capacitor C16
(0.33uF), C17 (1uF), C18 (0.22uF), C19 (1uF), C20 (0.22uF) and C21 (0.47uF) are constituted.
4) for the use of first passage and second channel, output signal z is obtained after second level operational amplifier circuit reduces 5 times
Output signalWherein first order amplifying circuit is by resistance R50 (10k Ω), R51 (10k Ω) and operational amplifier U13A
It constitutes, second level amplifying circuit is made of resistance R52 (50k Ω), R53 (10k Ω) and operational amplifier U14A.
From the foregoing, it will be observed that the present invention improves the design method of chaos hardware circuit, circuit using local range of decrease method
Lyapunov index is kept constant, good with the consistency of numerical simulation, and circuit structure is convenient, and chaos state is stablized, it is easy to accomplish,
In engineering field with good application prospect.
Claims (3)
1. a kind of fractional order nonlinear chaos system circuit, which is characterized in that including first passage circuit, second channel circuit and
Third channel circuit, first passage circuit are x, second channel circuit there are two input terminal, respectively y and z', an output end
There are three input terminal, respectively y', z' and x, two output ends, respectively y and y', third channel circuit has an input terminal to be
Y, an output end are z'；The input terminal of three channel circuits interconnects with output end, constitutes fractional order nonlinear
Chaos system circuit, input terminal x of the output end x of first passage circuit as second channel circuit, second channel circuit it is defeated
Outlet y is as the input terminal y of first passage circuit and the input terminal y of third channel circuit, the output end y' of second channel circuit
As the input terminal y' of second channel circuit, the output end z' of third channel circuit is as the input terminal z' of the first circuit passband and
The input terminal z' of two channel circuits；
The equivalent mathematical model of the circuit are as follows:
In formula, m1> 0.89, m2> 0.8, m3> 0.91, k > 0, x, y, z are the signal in nonlinear chaotic system circuit,For the m of x1Order derivative,For the m of y2Order derivative,For the m of z3Order derivative；
The first passage circuit include first resistor [R1], second resistance [R2], 3rd resistor [R3], the 4th resistance [R4],
5th resistance [R5], the 6th resistance [R6], the 7th resistance [R7], the 8th resistance [R8], the 9th resistance [R9], the tenth resistance
[R10], eleventh resistor [R11], twelfth resistor [R12], thirteenth resistor [R13], the 14th resistance [R14], the 15th
Resistance [R15], the 16th resistance [R16], the 17th resistance [R17], the 18th resistance [R18], the 19th resistance [19], first
Capacitor [C1], the second capacitor [C2], third capacitor [C3], the 4th capacitor [C4], the 5th capacitor [C5], the first multiplier [A1],
Second multiplier [A2], the first operational amplifier [U1A], second operational amplifier [U2A], third operational amplifier [U3A],
Four-operational amplifier [U4A] and the 5th operational amplifier [U5A]；Wherein two input terminals of the first multiplier [A1] are first logical
The input terminal y and input terminal z' of road circuit, the input terminal z' of first passage circuit and an input terminal of the second multiplier [A2]
Connection, the output end of the first multiplier [A1] are connect with another input terminal of the second multiplier [A2], the second multiplier [A2]
Output end is connect with the one end of first resistor [R1], the other end of first resistor [R1] and bearing for the first operational amplifier [U1A]
Input terminal connection, the positive input terminal of the first operational amplifier [U1A] is connected to ground, and the other end of first resistor [R1] is simultaneously with the
One end of two resistance [R2] connects, and the other end of second resistance [R2] is connect with the output end of the first operational amplifier [U1A], the
The other end of two resistance [R2] is connect with one end of 3rd resistor [R3] simultaneously, the other end and the 4th resistance of 3rd resistor [R3]
The one end of [R4] connects, and the other end of 3rd resistor [R3] is connect with the negative input end of second operational amplifier [U2A] simultaneously, the
The positive input terminal of two operational amplifiers [U2A] is connected to ground, the other end and second operational amplifier [U2A] of the 4th resistance [R4]
Output end connection, the other end of the 4th resistance [R4] connect with one end of the 5th resistance [R5] simultaneously, the 5th resistance [R5]
The other end is connect with one end of the 6th resistance [R6], and the other end of the 5th resistance [R5] connects with one end of the 8th resistance [R8] simultaneously
It connects, the other end of the 5th resistance [R5] is connect with one end of first capacitor [C1] simultaneously, and the other end of the 5th resistance [R5] is simultaneously
It being connect with one end of the second capacitor [C2], the other end of the 5th resistance [R5] is connect with one end of the 4th capacitor [C4] simultaneously, the
The other end of five resistance [R5] is connect with one end of the 5th capacitor [C5] simultaneously, the other end of the 5th resistance [R5] while and third
The negative input end of operational amplifier [U3A] connects, and the positive input terminal of third operational amplifier [U3A] is connected to ground, the 6th resistance
The other end of [R6] is connect with one end of the 7th resistance [R7], the other end of the 8th resistance [R8] and one end of the 9th resistance [R9]
Connection, the other end of the 9th resistance [R9] connect with one end of the tenth resistance [R10], the other end of the tenth resistance [R10] and the
One end of 11 resistance [R11] connects, and the other end of eleventh resistor [R11] is connect with one end of twelfth resistor [R12], the
The other end of 12 resistance [R12] is connect with one end of thirteenth resistor [R13], and the other end of twelfth resistor [R12] is simultaneously
It is connect with the other end of first capacitor [C1], one end of the other end of thirteenth resistor [R13] and the 14th resistance [R14] connects
Connect, the other end of the 14th resistance [R14] is connect with one end of the 15th resistance [R15], the other end of the second capacitor [C2] with
One end of third capacitor [C3] connects, and the other end of the 14th resistance [R14] is connect with the other end of third capacitor [C3] simultaneously,
The other end of 4th capacitor [C4] is connect with the other end of the 5th capacitor [C5], the other end of the 7th resistance [R7] and the 15th electricity
The other end connection of [R15] is hindered, the other end of the 7th resistance [R7] is connect with the other end of the 4th capacitor [C4] simultaneously, the 7th electricity
The other end for hindering [R7] is connect with the other end of the 5th capacitor [C5] simultaneously, and the other end of the 7th resistance [R7] is transported with third simultaneously
The output end connection of amplifier [U3A] is calculated, the other end of the 7th resistance [R7] connects with one end of the 16th resistance [R16] simultaneously
It connects, the other end of the 16th resistance [R16] is connect with one end of the 17th resistance [R17], the other end of the 16th resistance [R16]
It is connect simultaneously with the negative input end of four-operational amplifier [U4A], the positive input terminal and ground of four-operational amplifier [U4A] are even
It connects, the other end of the 17th resistance [R17] is connect with the output end of four-operational amplifier [U4A], four-operational amplifier
The output end of [U4A] is connect with one end of the 18th resistance [R18], the other end and the 19th resistance of the 18th resistance [R18]
The one end of [R19] connects, and the other end of the 18th resistance [R18] is connect with the negative input end of the 5th operational amplifier [U5A], the
The positive input terminal of five operational amplifiers [U5A] is connected to ground, the other end and the 5th operational amplifier of the 19th resistance [R19]
The output end of [U5A] connects, output end x of the output end of the 5th operational amplifier [U5A] as first passage circuit；
The second channel circuit include the 20th resistance [R20], the 21st resistance [R21], the 22nd resistance [R22],
23rd resistance [R23], the 24th resistance [R24], the 25th resistance [R25], the 26th resistance [R26], second
17 [R27], the 28th resistance [R28], the 29th resistance [R29], the 30th resistance [R30], the 31st resistance
[R31], the 32nd resistance [R32], the 33rd resistance [R33], the 34th resistance [R34], the 35th resistance
[R35], the 36th resistance [R36], the 37th resistance [R37], the 6th capacitor [C6], the 7th capacitor [C7], the 8th capacitor
[C8], the 9th capacitor [C9], the tenth capacitor [C10], the 11st capacitor [C11], the 12nd capacitor [C12], the 13rd capacitor
[C13], the 14th capacitor [C14], the 15th capacitor [C15], third multiplier [A3], the 6th operational amplifier [U6A], the 7th
Operational amplifier [U7A], the 8th operational amplifier [U8A], the 9th operational amplifier [U9A] and the tenth operational amplifier
[U10A]；One end of 20th resistance [R20] is the input terminal y' of second channel circuit, the other end of the 20th resistance [R20]
Connect with one end of the 21st resistance [R21], the other end of the 20th resistance [R20] simultaneously with the 6th operational amplifier
The negative input end of [U6A] connects, and the positive input terminal of the 6th operational amplifier [U6A] is connected to ground, the 21st resistance [R21]
The other end is connect with the output end of the 6th operational amplifier [U6A], and the other end of the 21st resistance [R21] is simultaneously with the 20th
One end of two resistance [R22] connects, and the other end of the 22nd resistance [R22] is connect with one end of the 23rd resistance [R23],
Two input terminals of third multiplier [A3] are respectively the input terminal z' and input terminal x of second channel circuit, third multiplier
The output end of [A3] is connect with one end of the 24th resistance [R24], the other end of the 24th resistance [R24] and the 7th operation
The negative input end of amplifier [U7A] connects, and the positive input terminal of the 7th operational amplifier [U7A] is connected to ground, the 24th resistance
The other end of [R24] is connect with one end of the 25th resistance [R25] simultaneously, the other end of the 25th resistance [R25] and the
The output ends of seven operational amplifiers [U7A] connects, the other end of the 25th resistance [R25] simultaneously with the 26th resistance
The one end of [R26] connects, and the other end of the 26th resistance [R26] is connect with the other end of the 23rd resistance [R23], and second
The other ends of 16 resistance [R26] is connect with one end of the 27th resistance [R27] simultaneously, the 27th resistance [R27] it is another
One end is connect with one end of the 28th resistance [R28], the other end and the 29th resistance of the 28th resistance [R28]
The one end of [R29] connects, and the other end of the 29th resistance [R29] is connect with one end of the 30th resistance [R30], the 30th electricity
The other end of resistance [R30] is connect with one end of the 31st resistance [R31], the other end and third of the 31st resistance [R31]
One end of 12 resistance [R32] connects, and the other end of the 32nd resistance [R32] and one end of the 33rd resistance [R33] connect
It connects, the other end of the 26th resistance [R26] is connect with one end of the 6th capacitor [C6] simultaneously, the other end of the 6th capacitor [C6]
Connect with the other end of the 29th resistance [R29], the other end of the 26th resistance [R26] simultaneously with the 7th capacitor [C7]
One end connection, the other end of the 7th capacitor [C7] are connect with the other end of the 29th resistance [R29], the 26th resistance
The other end of [R26] is connect with one end of the 8th capacitor [C8] simultaneously, the other end and the 29th resistance of the 8th capacitor [C8]
The other end of [R29] connects, and the other end of the 26th resistance [R26] is connect with one end of the 9th capacitor [C9] simultaneously, and the 9th
The other end of capacitor [C9] is connect with the other end of the 29th resistance [R29], and the other end of the 26th resistance [R26] is simultaneously
It is connect with one end of the tenth capacitor [C10], the other end of the tenth capacitor [C10] and the other end of the 31st resistance [R31] connect
It connects, the other end of the 26th resistance [R26] is connect with one end of the 11st capacitor [C11] simultaneously, the 11st capacitor [C11]
The other end is connect with the other end of the 31st resistance [R31], and the other end of the 26th resistance [R26] is electric with the 12nd simultaneously
Holding one end connection of [R12], the other end of the 12nd capacitor [R12] is connect with the other end of the 31st resistance [R31], and second
The other end of 16 resistance [R26] is connect with one end of the 13rd capacitor [C13] simultaneously, the other end of the 13rd capacitor [C13]
Connect with the other end of the 33rd resistance [R33], the other end of the 26th resistance [R26] simultaneously with the 14th capacitor
The one end of [C14] connects, and the other end of the 14th capacitor [C14] is connect with the other end of the 33rd resistance [R33], and the 20th
The other ends of six resistance [R26] connect with one end of the 15th capacitor [C15] simultaneously, the other end of the 15th capacitor [C15] and
The other end of 33rd resistance [R33] connects, the other end of the 26th resistance [R26] simultaneously with the 8th operational amplifier
The negative input end of [U8A] connects, and the positive input terminal of the 8th operational amplifier [U8A] is connected to ground, the 8th operational amplifier [U8A]
Output end connect with the other end of the 33rd resistance [R33], the output end of the 8th operational amplifier [U8A] is logical as second
The output end y' of the output end y' of road circuit, second channel circuit are connect with one end of the 34th resistance [R34] simultaneously, third
The other end of 14 resistance [R34] is connect with one end of the 35th resistance [R35], the other end of the 34th resistance [R34]
It is connect simultaneously with the negative input end of the 9th operational amplifier [U9A], the positive input terminal and ground of the 9th operational amplifier [U9A] are even
It connects, the other end of the 35th resistance [R35] is connect with the output end of the 9th operational amplifier [U9A], the 35th resistance
The other end of [R35] is connect with one end of the 36th resistance [R36] simultaneously, the other end of the 36th resistance [R36] and the
One end of 37 resistance [R37] connects, the other end of the 36th resistance [R36] simultaneously with the tenth operational amplifier [U10A]
Negative input end connection, the positive input terminal of the tenth operational amplifier [U10A] is connected to ground, the 37th resistance [R37] it is another
End is connect with the output end of the tenth operational amplifier [U10A], and the output end of the tenth operational amplifier [U10A] is as second channel
The output end y of circuit；
The third channel circuit include slide rheostat [R38], the 38th resistance [R39], the 39th resistance [R40],
40th resistance [R41], the 41st resistance [R42], the 42nd resistance [R43], the 43rd resistance [R44], the 40th
Four resistance [R45], the 45th resistance [R46], the 46th resistance [R47], the 47th resistance [R48], the 48th electricity
Hinder [R49], the 49th resistance [R50], the 50th resistance [R51], the 51st resistance [R52], the 52nd resistance
[R53], the 16th capacitor [C16], the 17th capacitor [C17], the 18th capacitor [C18], the 19th capacitor [C19], the 20th
Capacitor [C20], the 21st capacitor [C21], first diode [D1], the second diode [D2], the 11st operational amplifier
[U11A], the 12nd operational amplifier [U12A], the 13rd operational amplifier [U13A] and the tenth four-operational amplifier [U14A]；
Input terminal y of one fixing end of slide rheostat [R38] as third channel circuit, the sliding end of slide rheostat [R38]
It is connect with the anode of first diode [D1], the negative terminal of first diode [D1] and bearing for the 11st operational amplifier [U11A] are defeated
Enter end connection, the positive input terminal of the 11st operational amplifier [U11A] is connected to ground, the negative terminal of first diode [D1] simultaneously with
One end of 38th resistance [R39] connects, and the anode of first diode [D1] connects with the negative terminal of the second diode [D2] simultaneously
It connects, the other end of the 38th resistance [R39] is connect with the output end of the 11st operational amplifier [U11A], the 38th resistance
The other end of [R39] is connect with one end of the 39th resistance [R40] simultaneously, the other end of the 39th resistance [R40] and the
The anode of two diodes [D2] connects, and the other end of the 39th resistance [R40] connects with one end of the 40th resistance [R41] simultaneously
It connects, the other end of the 39th resistance [R40] is connect with one end of the 41st resistance [R42] simultaneously, the 41st resistance
The other end of [R42] is connect with one end of the 42nd resistance [R43], the other end and the 40th of the 42nd resistance [R43]
One end of three resistance [R44] connects, and the other end of the 43rd resistance [R44] is connect with one end of the 44th resistance [R45],
The other end of 44th resistance [R45] is connect with one end of the 45th resistance [R46], the 45th resistance [R46] it is another
One end is connect with one end of the 46th resistance [R47], the other end and the 47th resistance of the 46th resistance [R47]
The one end of [R48] connects, and the other end of the 47th resistance [R48] is connect with one end of the 48th resistance [R49], and the 30th
The other ends of nine resistance [R40] connect with one end of the 16th capacitor [C16] simultaneously, the other end of the 16th capacitor [C16] and
One end of 17th capacitor [C17] connects, the other end of the 17th capacitor [C17] and the other end of the 45th resistance [R46]
The other end of connection, the 39th resistance [R40] is connect with one end of the 18th capacitor [C18] simultaneously, the 18th capacitor [C18]
The other end connect with one end of the 19th capacitor [C19], the other end and the 47th resistance of the 19th capacitor [C19]
The other end of [R48] connects, and the other end of the 39th resistance [R40] is connect with one end of the 20th capacitor [C20] simultaneously, the
The other end of 20 capacitors [C20] is connect with the other end of the 48th resistance [R49], the 39th resistance [R40] it is another
End is connect with one end of the 21st capacitor [C21] simultaneously, the other end and the 48th resistance of the 21st capacitor [C21]
The other end of [R49] connects, and the other end of the 39th resistance [R40] is defeated with bearing for the 12nd operational amplifier [U12A] simultaneously
Enter end connection, [positive input terminal of U12A is connected to ground the 12nd operational amplifier, the 12nd operational amplifier [output of U12A
End is connect with the other end of the 48th resistance [R49], the other end and the 48th resistance [R49] of the 40th resistance [R41]
Other end connection, the other ends of 40 resistance [R41] connect with one end of the 49th resistance [R50] simultaneously, the 49th
The other end of resistance [R50] is connect with one end of the 50th resistance [R51], the other end of the 49th resistance [R50] simultaneously with
The negative input end of 13rd operational amplifier [U13A] connects, and the positive input terminal and ground of the 13rd operational amplifier [U13A] are even
It connects, the other end of 50 resistance [R51] is connect with the output end of the 13rd operational amplifier [U13A], the 13rd operational amplifier
The output end of [U13A] is connect with one end of the 51st resistance [R52] simultaneously, the other end of the 51st resistance [R52] and the
One end of 52 resistance [R53] connects, the other end of the 51st resistance [R52] simultaneously with the tenth four-operational amplifier
The negative input end of [U14A] connects, and the positive input terminal of the tenth four-operational amplifier [U14A] is connected to ground, the 52nd resistance
Output end z' of the other end of [R53] as third channel circuit.
2. fractional order nonlinear chaos system circuit according to claim 1, which is characterized in that all operational amplifiers
Model it is all the same, power supply be ± 15V DC power supply.
3. fractional order nonlinear chaos system circuit according to claim 1, which is characterized in that first resistor [R1],
Three resistance [R3], the 16th resistance [R16], the 17th resistance [R17], the 18th resistance [R18], the 20th resistance [R20],
21 resistance [R21], the 24th resistance [R24], the 34th resistance [R34], the 35th resistance [R35], the 30th
Six resistance [R36], the 38th resistance [R39], the 39th resistance [R40], the 49th resistance [R50], the 50th resistance
[R51] and the 52nd resistance [R53] are 10k Ω, second resistance [R2], the 4th resistance [R4], the 25th resistance
[R25], the 26th resistance [R26] and the 40th resistance [R41] are 100k Ω, the 5th resistance [R5] be 500k Ω, the 6th
Resistance [R6] be 30k Ω, the 7th resistance [7] be 5.6k Ω, the 8th resistance [R8], the 9th resistance [R9], the tenth resistance [R10],
27th resistance [R27], the 28th resistance [R28], the 41st resistance [R42], the 42nd resistance [R43] and the 4th
13 resistance [R44] are 22M Ω, and eleventh resistor [R11] is 15M Ω, and twelfth resistor [R12] is 931k Ω, and the 13rd
Resistance [R13] is 1.2M Ω, and the 14th resistance [R14] is 20k Ω, and the 15th resistance [R15] is 3.9k Ω, the 19th resistance
[R19] is 250k Ω, and the 22nd resistance [R22] is 82k Ω, and the 23rd resistance [R23] is 1.3k Ω, the 29th resistance
[R29] is 681k Ω, and the 30th resistance [R30] is 5.1M Ω, and the 31st resistance [R31] is 78.8k Ω, the 32nd resistance
[R32] is 240k Ω, and the 33rd resistance [R33] is 11k Ω, and the 37th resistance [R37] and the 51st resistance [R52] are equal
For 50k Ω, the 44th resistance [R45] is 9.1M Ω, and the 45th resistance [R46] is 732k Ω, the 46th resistance [R47]
For 3.3M Ω, the 47th resistance [R48] is 261k Ω, and the 48th resistance [R49] is 36.5k Ω, slide rheostat [R38]
Maximum value be 200k Ω, first capacitor [C1], the 4th capacitor [C4], the 15th capacitor [C15], the 18th capacitor [C18],
20th capacitor [C20] is 0.22uF, and the second capacitor [C2] and the 16th capacitor [C16] are 0.33uF, third capacitor
[C3], the 5th capacitor [C5] and the 21st capacitor [C21] are 0.47uF, and the 6th capacitor [C6] and the tenth capacitor [C10] are equal
For 0.1uF, the 7th capacitor [C7], the 8th capacitor [C8], the 11st capacitor [C11], the 12nd capacitor [C12], the 13rd capacitor
[C13] and the 14th capacitor [C14] are 0.15uF, and the 9th capacitor [C9] is 0.3uF, the 17th capacitor [C17] and the 19th
Capacitor [C19] is 1uF.
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| CN107124263B (en) * | 2017-06-30 | 2020-02-21 | 湘潭大学 | Nested multi-scroll chaotic circuit |
| CN108509704B (en) * | 2018-03-22 | 2019-08-20 | 武汉科技大学 | A kind of fractional order recalls the equivalent circuit of sensor |
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