CN106817213A - 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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- CN106817213A CN106817213A CN201510848949.1A CN201510848949A CN106817213A CN 106817213 A CN106817213 A CN 106817213A CN 201510848949 A CN201510848949 A CN 201510848949A CN 106817213 A CN106817213 A CN 106817213A
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- 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 circuit of new fractional order with absolute value term, including first passage circuit, second channel circuit and third channel circuit, first passage circuit has two inputs, one output end, second channel circuit has three inputs, two output ends, third channel circuit has an input, an output end；Three inputs of channel circuit interconnect with output end, constitute fractional order nonlinear chaos system circuit, the output end of first passage circuitAs the input of second channel circuit, the output end of second channel circuit is used as the input of first passage circuit and the input of third channel circuit, the output end of second channel circuit as second channel circuit input, the output end of third channel circuit is used as the input of the first circuit passband and the input of second channel circuit.The discontinuous chaos system, construction is convenient, chaos state stabilization, it is easy to accomplish, there is preferable application prospect in engineering field.
Description
Technical field
The invention belongs to field of information encryption, particularly a kind of fractional order nonlinear chaos system circuit.
Background technology
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 change the world outlook of people, it allows people's thinking to come to life, it is considered to problem more comprehensively,
Rationality.Scholars generally believe：Non-linear to be mainly made up of three parts, they are respectively chaos, point shape and orphan, therefore, mix
Ignorant theory is held the balance in non-linear subject.Progress of the research chaos system to science and technology has huge potential value.
Chaos is a kind of determination sexual behaviour that a Kind of Nonlinear Dynamical System for determining is showed, and is regular
The performance of irregular motion in system.Professor Lorenz in 1963 is found that first chaos system and is named as Lorenz and mixes
Ignorant system.The proposition of the system means the origin of Chaos, and a hot topic of scientists study is turned into from this chaotic motion
Field.The research of chaos system develops with rapid changepl. never-ending changes and improvements, and scholars are found that increasing new type of chaotic system, these
The proposition of new system promotes the development of chaology.For example, R ssler systems, Chua ' s circuits, Chen systems, L ü chaos
System.In recent years, researcher constantly explores to new fractional-order system, and increasing new fractional-order system is constantly suggested, and such as divides
Number rank Chua ' s circuits, fractional order R ssler chaos systems, fractional order Lorenz chaos systems, fractional order unified system,
Fractional order L ü chaos systems etc..
With the discovery of chaos system, the research of the Chaotic Synchronous little by little heat subject as researcher, people also by
Gradually propose more and more feasible, methods of Synchronization Control for using.Chaotic Synchronous are applied to the every field of life,
Such as secret communication, therapeutic treatment, bioengineering.
At present, most researchs carry out system model based on computer emulation method realization frequently with Matlab simulation softwares
With control method emulation, circuit structure emulation is carried out using Multisim simulation softwares.But numerical simulation and side circuit structure
Make and still suffer from certain otherness, especially limited by the physical characteristic of actual components, the chaos circuit of theory deduction is not
Necessarily can successfully reappear in side circuit.
The content of the invention
It is an object of the invention to provide a kind of fractional order nonlinear chaos system circuit.
The technical solution for realizing the object of the invention is：A kind of fractional order nonlinear chaos system circuit, including first
Channel circuit, second channel circuit and third channel circuit, first passage circuit have two inputs, respectively y and z', one
Output end is x, and second channel circuit has three inputs, respectively y', z' and x, two output ends, respectively y and y', the 3rd
Channel circuit has an input for y, and an output end is z'；Three inputs of channel circuit are interconnected on output end
Together, constitute fractional order nonlinear chaos system circuit, the output end x of first passage circuit as second channel circuit input
End x, the output end y of second channel circuit as the input y of the first passage circuit and input y of third channel circuit, the
The output end y' of two channel circuits as second channel circuit input y', the output end z' of third channel circuit is used as first
The input z' of the circuit passband and input z' of second channel circuit；
The equivalent mathematical model of the circuit is：
In formula, m1>0.89, m2>0.8, m3>0.91, k>0, x, y, z is the signal in nonlinear chaotic system circuit,It is the m of x1Order derivative,It is the m of y2Order derivative,It is the m of z3Order derivative.
It is of the invention compared with existing chaos system and building method, its remarkable advantage is：1) chaos system proposed by the present invention
System has fractional order chaotic characteristic, is more suitable for being applied in secret communication field；2) chaos system proposed by the present invention is using exhausted
The quadratic term in original system is instead of to value item, 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 causes that the output voltage amplitude of novel circuit first passage and second channel is adjustable, can pass through
Adjustable resistance is flexibly set, for circuit application is provided conveniently；4) circuit system ensure that system during amplitude regulation
Lyapunov indexes it is constant, thus circuit chaotic characteristic keep it is constant, be conducive to systematic difference；5) present invention uses office
Portion's range of decrease method improves the method for designing of chaos hardware circuit, and the uniformity with numerical simulation is good, and circuit structure is convenient, chaos shape
State stabilization, it is easy to accomplish, there is preferable application prospect in engineering field.
Brief description of the drawings
Fig. 1 is fractional order nonlinear chaos system circuit entire block diagram of the invention.
Fig. 2 is the coexisting attractors of new chaotic systems with fractional order proposed by the present invention.
Fig. 3 is the circuit theory diagrams of new chaotic systems with fractional order first passage proposed by the present invention.
Fig. 4 is the circuit theory diagrams of new chaotic systems with fractional order second channel proposed by the present invention.
Fig. 5 is the circuit theory diagrams of new chaotic systems with fractional order third channel proposed by the present invention.
Fig. 6 is the Lyapunov index curve diagrams of chaotic systems with fractional order proposed by the present invention.
Specific embodiment
With reference to Fig. 1, a kind of fractional order nonlinear chaos system circuit of the invention, including first passage circuit, second lead to
Road circuit and third channel circuit, first passage circuit have two inputs, and respectively y and z' a, output end is x, second
Channel circuit has three inputs, respectively y', z' and x, and two output ends, respectively y and y', third channel circuit has one
Input is y, and an output end is z'；Three inputs of channel circuit interconnect with output end, constitute fraction
Rank nonlinear chaotic system circuit, the output end x of first passage circuit as second channel circuit input x, second channel
The output end y of circuit as the input y of the first passage circuit and input y of third channel circuit, second channel circuit
Output end y' as second channel circuit input y', the output end z' of third channel circuit as the first circuit passband input
The input z' of end z' and second channel circuit；
The equivalent mathematical model of the circuit is：
In formula, m1>0.89, m2>0.8, m3>0.91, k>0, x, y, z is the signal in nonlinear chaotic system circuit,It is the m of x1Order derivative,It is the m of y2Order derivative,It is the m of z3Order derivative.
With reference to 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, the 12nd resistance R12, the 13rd resistance 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, the first electric capacity C1, the second electric capacity C2, the 3rd electric capacity
C3, the 4th electric capacity C4, the 5th electric capacity C5, the first multiplier A1, the second multiplier A2, the first operational amplifier U1A, the second computing
Amplifier U2A, the 3rd operational amplifier U3A, four-operational amplifier U4A and the 5th operational amplifier U5A；Wherein the first multiplication
Two inputs of device A1 are the input y and input z' of first passage circuit, the input z' of first passage circuit and the
One input connection of paired multiplier A2, the output end of the first multiplier A1 connects with another input of the second multiplier A2
Connect, the output end of the second multiplier A2 is connected with one end of first resistor R1, and the other end of first resistor R1 is put with the first computing
The negative input end connection of big device U1A, the positive input terminal of the first operational amplifier U1A is connected to ground, the other end of first resistor R1
It is connected with one end of second resistance R2 simultaneously, the other end of second resistance R2 is connected with the output end of the first operational amplifier U1A,
The other end of second resistance R2 is connected with one end of 3rd resistor R3 simultaneously, the other end of 3rd resistor R3 and the 4th resistance R4's
One end connects, and the other end of 3rd resistor R3 is connected with the negative input end of the 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 connected with the output end of the second operational amplifier U2A, the
The other end of four resistance R4 is connected with one end of the 5th resistance R5 simultaneously, the other end of the 5th resistance R5 and the one of the 6th resistance R6
End connection, the other end of the 5th resistance R5 be connected with one end of the 8th resistance R8 simultaneously, the other end of the 5th resistance R5 and meanwhile with
One end connection of the first electric capacity C1, the other end of the 5th resistance R5 is connected with one end of the second electric capacity C2 simultaneously, the 5th resistance R5
The other end be connected with one end of the 4th electric capacity C4 simultaneously, the other end of the 5th resistance R5 simultaneously with one end company of the 5th electric capacity C5
Connect, the other end of the 5th resistance R5 is connected with the negative input end of the 3rd operational amplifier U3A simultaneously, the 3rd operational amplifier U3A
Positive input terminal be connected to ground, the other end of the 6th resistance R6 is connected with one end of the 7th resistance R7, and the 8th resistance R8's is another
End is connected with one end of the 9th resistance R9, and the other end of the 9th resistance R9 is connected with one end of the tenth resistance R10, the tenth resistance
The other end of R10 is connected with one end of the 11st resistance R11, the other end of the 11st resistance R11 and the one of the 12nd resistance R12
End connection, the other end of the 12nd resistance R12 is connected with one end of the 13rd resistance R13, and the other end of the 12nd resistance R12 is same
When be connected with the other end of the first electric capacity C1, the other end of the 13rd resistance R13 is connected with one end of the 14th resistance R14,
The other end of 14 resistance R14 is connected with one end of the 15th resistance R15, the other end of the second electric capacity C2 and the 3rd electric capacity C3's
One end connects, and the other end of the 14th resistance R14 is connected with the other end of the 3rd electric capacity C3 simultaneously, the other end of the 4th electric capacity C4
The other end with the 5th electric capacity C5 is connected, and the other end of the 7th resistance R7 is connected with the other end of the 15th resistance R15, the 7th electricity
The other end for hindering R7 is connected with the other end of the 4th electric capacity C4 simultaneously, and the other end of the 7th resistance R7 is simultaneously with the 5th electric capacity C5's
The other end is connected, and the other end of the 7th resistance R7 is connected with the output end of the 3rd operational amplifier U3A simultaneously, the 7th resistance R7's
The other end is connected with one end of the 16th resistance R16 simultaneously, the other end of the 16th resistance R16 and the one of the 17th resistance R17
End connection, the other end of the 16th resistance R16 is connected with the negative input end of four-operational amplifier U4A simultaneously, and the 4th computing 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 connected with one end of the 18th resistance R18, the other end of the 18th resistance R18 with
One end connection of the 19th resistance R19, the other end of the 18th resistance R18 and the negative input end of the 5th operational amplifier U5A connect
Connect, 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 connection of U5A, the output end of the 5th operational amplifier U5A as first passage circuit output end x.
With reference to Fig. 4, the second channel circuit includes the 20th resistance R20, the 21st resistance R21, the 22nd electricity
Resistance 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, the 3rd
17 resistance R37, the 6th electric capacity C6, the 7th electric capacity C7, the 8th electric capacity C8, the 9th electric capacity C9, the tenth electric capacity C10, the 11st electricity
Hold C11, the 12nd electric capacity C12, the 13rd electric capacity C13, the 14th electric capacity C14, the 15th electric capacity C15, the 3rd 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 y' of second channel circuit, and the 20th resistance R20's is another
End is connected 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 is connected, and 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 connection of six operational amplifier U6A, 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 is connected with one end of the 23rd resistance R23, two of the 3rd multiplier A3
Input is respectively the input z' and input x of second channel circuit, the output end of the 3rd multiplier A3 and the 24th electricity
One end connection of R24 is hindered, the other end of the 24th resistance R24 is connected with the negative input end of the 7th operational amplifier U7A, 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 is connected with the output end of the 7th operational amplifier U7A, and the 25th is electric
The other end for hindering R25 is connected with one end of the 26th resistance R26 simultaneously, the other end and the 20th of the 26th resistance R26
The other end connection of three resistance R23, the other end of the 26th resistance R26 is connected with one end of the 27th resistance R27 simultaneously,
The other end of the 27th resistance R27 is connected with one end of the 28th resistance R28, the other end of the 28th resistance R28 with
One end connection of the 29th resistance R29, the other end of the 29th resistance R29 is connected with one end of the 30th resistance R30, the
The other end of 30 resistance R30 is connected with one end of the 31st resistance R31, the other end and the 3rd of the 31st resistance R31
One end connection of 12 resistance R32, the other end of the 32nd resistance R32 is connected with one end of the 33rd resistance R33, and second
The other end of 16 resistance R26 be connected with one end of the 6th electric capacity C6 simultaneously, the other end of the 6th electric capacity C6 and the 29th electric
The other end connection of R29 is hindered, the other end of the 26th resistance R26 is connected with one end of the 7th electric capacity C7 simultaneously, the 7th electric capacity
The other end of C7 is connected with the other end of the 29th resistance R29, the other end of the 26th resistance R26 simultaneously with the 8th electric capacity
One end connection of C8, the other end of the 8th electric capacity C8 is connected with the other end of the 29th resistance R29, the 26th resistance R26
The other end simultaneously be connected with one end of the 9th electric capacity C9, the other end of the 9th electric capacity C9 is another with the 29th resistance R29
End connection, the other end of the 26th resistance R26 is connected with one end of the tenth electric capacity C10 simultaneously, the other end of the tenth electric capacity C10
The other end with the 31st resistance R31 is connected, the other end of the 26th resistance R26 simultaneously with the 11st electric capacity C11 one
End connection, the other end of the 11st electric capacity C11 is connected with the other end of the 31st resistance R31, and the 26th resistance R26's is another
One end is connected with one end of the 12nd electric capacity R12 simultaneously, and the other end of the 12nd electric capacity R12 is another with the 31st resistance R31
One end connects, and the other end of the 26th resistance R26 is connected with one end of the 13rd electric capacity C13 simultaneously, the 13rd electric capacity C13's
The other end is connected with the other end of the 33rd resistance R33, the other end of the 26th resistance R26 simultaneously with the 14th electric capacity
One end connection of C14, the other end of the 14th electric capacity C14 is connected with the other end of the 33rd resistance R33, the 26th resistance
The other end of R26 is connected with one end of the 15th electric capacity C15 simultaneously, the other end and the 33rd resistance of the 15th electric capacity C15
The other end connection of R33, the other end of the 26th resistance R26 is connected with the negative input end of the 8th operational amplifier U8A simultaneously,
The positive input terminal of the 8th operational amplifier U8A is connected to ground, output end and the 33rd resistance of the 8th operational amplifier U8A
The other end connection of R33, the output end of the 8th operational amplifier U8A as second channel circuit output end y', second channel
The output end y' of circuit is connected with one end of the 34th resistance R34 simultaneously, the other end and the 30th of the 34th resistance R34
One end connection of five resistance R35, the other end of the 34th resistance R34 negative input end simultaneously with the 9th operational amplifier U9A
Connection, the positive input terminal of the 9th operational amplifier U9A is connected to ground, and the other end and the 9th computing of the 35th resistance R35 are put
The output end connection of big device U9A, the other end of the 35th resistance R35 is connected with one end of the 36th resistance R36 simultaneously, the
The other end of 36 resistance R36 is connected with one end of the 37th resistance R37, and the other end of the 36th resistance R36 is simultaneously
Negative input end with the tenth operational amplifier U10A is connected, and the positive input terminal of the tenth operational amplifier U10A is connected to ground, and the 3rd
The other end of 17 resistance R37 is connected with the output end of the tenth operational amplifier U10A, and the tenth operational amplifier U10A's is defeated
Go out output end y of the end as second channel circuit.
With reference to Fig. 5, the third channel circuit includes slide rheostat R38, the 38th resistance R39, the 39th electricity
Resistance 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 electric capacity C16, the tenth
Seven electric capacity C17, the 18th electric capacity C18, the 19th electric capacity C19, the 20th electric capacity C20, the 21st electric capacity 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；One fixing end of slide rheostat R38 as third channel circuit input
Y, the sliding end of slide rheostat R38 is connected with the anode of the first diode D1, and the negative terminal of the first diode D1 and the 11st is transported
The negative input end connection of amplifier U11A is calculated, the positive input terminal of the 11st operational amplifier U11A is connected to ground, the first diode
The negative terminal of D1 be connected with one end of the 38th resistance R39 simultaneously, the anode of the first diode D1 and meanwhile with the second diode
The negative terminal connection of D2, the other end of the 38th resistance R39 is connected with the output end of the 11st operational amplifier U11A, and the 30th
The other end of eight resistance R39 is connected with one end of the 39th resistance R40 simultaneously, the other end of the 39th resistance R40 and the
The anode connection of two diode D2, the other end of the 39th resistance R40 is connected with one end of the 40th resistance R41 simultaneously, the
The other end of 39 resistance R40 is connected with one end of the 41st resistance R42 simultaneously, the other end of the 41st resistance R42
One end with the 42nd resistance R43 is connected, and the other end of the 42nd resistance R43 and one end of the 43rd resistance R44 connect
Connect, the other end of the 43rd resistance R44 is connected with one end of the 44th resistance R45, the other end of the 44th resistance R45
One end with the 45th resistance R46 is connected, and the other end of the 45th resistance R46 and one end of the 46th resistance R47 connect
Connect, the other end of the 46th resistance R47 is connected with one end of the 47th resistance R48, the other end of the 47th resistance R48
One end with the 48th resistance R49 is connected, the other end of the 39th resistance R40 one end simultaneously with the 16th electric capacity C16
Connection, the other end of the 16th electric capacity C16 is connected with one end of the 17th electric capacity C17, the other end of the 17th electric capacity C17 and the
The other end connection of 45 resistance R46, the other end of the 39th resistance R40 connects with one end of the 18th electric capacity C18 simultaneously
Connect, the other end of the 18th electric capacity C18 is connected with one end of the 19th electric capacity C19, the other end and the 4th of the 19th electric capacity C19
The other end connection of 17 resistance R48, the other end of the 39th resistance R40 is connected with one end of the 20th electric capacity C20 simultaneously,
The other end of the 20th electric capacity C20 is connected with the other end of the 48th resistance R49, and the other end of the 39th resistance R40 is same
When be connected with one end of the 21st electric capacity C21, the other end of the 21st electric capacity C21 is another with the 48th resistance R49
End connection, the other end of the 39th resistance R40 is connected 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, output end and the 48th resistance of the 12nd operational amplifier U12A
The other end connection of R49, the other end of the 40th resistance R41 is connected with the other end of the 48th resistance R49,40 resistance
The other end of R41 be connected with one end of the 49th resistance R50 simultaneously, the other end of the 49th resistance R50 and the 50th electric
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
Connect, the positive input terminal of the 13rd operational amplifier U13A is connected to ground, the other end and the 13rd computing of 50 resistance R51 are put
The output end connection of big device U13A, the output end of the 13rd operational amplifier U13A one end simultaneously with the 51st resistance R52
Connection, the other end of the 51st resistance R52 is connected with one end of the 52nd resistance R53, and the 51st resistance R52's is another
End is connected with the negative input end of the tenth four-operational amplifier U14A simultaneously, positive input terminal and the ground of the tenth four-operational amplifier U14A
Connection, the other end of the 52nd resistance R53 as third channel circuit output end z'.
The model all same of above-mentioned all of operational amplifier, its power supply is ± 15V dc sources.
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
Resistance 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, 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 the 11st resistance R11 is
15M Ω, the 12nd resistance R12 are 931k Ω, and the 13rd resistance R13 is 1.2M Ω, and the 14th resistance R14 is 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 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 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, the first electric capacity C1, the 4th electric capacity C4, the 15th electric capacity C15, the 18th electric capacity C18, the 20th electric capacity
C20 is 0.22uF, and the second electric capacity C2 and the 16th electric capacity C16 is 0.33uF, the 3rd electric capacity C3, the 5th electric capacity C5 and second
11 electric capacity C21 are 0.47uF, and the 6th electric capacity C6 and the tenth electric capacity C10 is 0.1uF, the 7th electric capacity C7, the 8th electric capacity C8,
11st electric capacity C11, the 12nd electric capacity C12, the 13rd electric capacity C13 and the 14th electric capacity C14 are 0.15uF, the 9th electric capacity C9
It is 0.3uF, the 17th electric capacity C17 and the 19th electric capacity C19 are 1uF.
The new discontinuous chaos system of fractional order of the invention and its circuit structure are carried out in detail below in conjunction with brief description of the drawings
Thin description.
A kind of discontinuous chaos system of new fractional order and its circuit structure construction method, specially：
Step 1, the block mold for proposing the new discontinuous three-dimensional chaotic system of integer rank.
1) model of the former integer continuous three-dimensional chaotic system of rank is：
2) improved model of the discontinuous chaos system of new fractional order is：
In formula, m1>0.89,m2>0.8,m3>Variable (the k of 0.91, k value>0).The coexisting attractors of novel system are shown in Fig. 2.
Step 2, the general structure for designing new discontinuous chaos circuit, are made up of three channel circuits：
1) first passage is made up of multiplier A1, A2, operational amplifier U1A, U2A, U3A, U4A, U5A and resistance, electric capacity.
2) second channel is made up of multiplier A3, operational amplifier U6A, U7A, U8A, U9A, U10A and resistance, electric capacity.
3) third channel is made up of diode D1, D2, operational amplifier U11A, U12A, U13A, U14A and resistance, electric capacity.
4) final output signal of whole system is x, y, z, is effectively transmitted for signal and exported, and intermediate node signal is
x'、y'、z'。
Step 3, design first passage circuit structure, first passage final output signal is 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
Constitute as follows：
1) second channel output valve y and third channel output signal z' are input to multiplier A1, A1 output signal and z' is defeated
Enter to multiplier A2, obtain output signal a=0.01yz'2。
2) because two-stage multiplier causes that output signal reduces 100 times, it is therefore desirable to which output signal a is amplified.Signal a is passed through
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 is exported, so as to obtainI.e.
4) fractional order circuit is made up of a series of resistance capacitances.In the circuit that the present invention is announced, first passage is with m1=
As a example by 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), electric capacity C1 (0.22uF), C2 (0.33uF), C3 (0.47uF), C4 (0.22uF), C5
(0.47uF) is constituted.
5) after signal x' amplifies 25 times through dual-stage amplifier circuit, first passage output signal x=25x' is obtained, i.e.,First order amplifying circuit is by resistance R16 (10k Ω), R16 (10k Ω) and operational amplifier U4A structures
Into second level amplifying circuit is made up of resistance R18 (10k Ω), R19 (250k Ω) and operational amplifier U5A.
6) it may be noted that third channel construction process in, z=5z', then
Realize the function of first passage in system model.
Step 4, design second channel circuit structure, second channel final output signal is y and y'.Second channel is by multiplication
Device A3, operational amplifier U6A, U7A, U8A, U9A, U10A and resistance, electric capacity are constituted, as shown in Figure 4.Second channel circuit is specific
Constitute 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), through R22 (82k Ω), R23 (1.3k Ω), after signal e is through R22 (82k Ω), common input fractional order is electric for signal c
Road and operational amplifier U8A, so as to obtainI.e.
5) fractional order circuit is made up of a series of resistance capacitances.In the circuit that the present invention is announced, second channel is with m2=
As a example by 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), electric capacity 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) after signal y' amplifies 5 times through second amplifying circuit, output signal y=5y' is obtained, i.e.,Wherein 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 up of resistance R36 (10k Ω), R37 (50k Ω) and operational amplifier U10A.
7) it may be noted that third channel construction process in, z=5z', thenRealize system mould
The function of second channel in type.
Step 5, design third channel circuit structure, second channel final output signal is 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
Constitute 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 output f=k | y |, wherein diode D1,
D2 and operational amplifier U11A main composition absolute value circuits, slide rheostat R38 constitute the function of model adjustable parameter k.With k
As a example by=8, R38 resistances are 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 m3As a example by=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), electric capacity 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, after output signal z reduces 5 times through two grades of discharge circuits, obtain
Output signalWherein first order amplifying circuit is by resistance R50 (10k Ω), R51 (10k Ω) and operational amplifier U13A
Constitute, second level amplifying circuit is made up 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 method for designing of chaos hardware circuit, circuit using local range of decrease method
Lyapunov indexes keep constant, and the uniformity with numerical simulation is good, and circuit structure is convenient, chaos state stabilization, it is easy to accomplish,
There is preferable application prospect in engineering field.
Claims (6)
1. a kind of fractional order nonlinear chaos system circuit, it is characterised in that including first passage circuit, second channel circuit and
Third channel circuit, first passage circuit has two inputs, and respectively y and z' a, output end is x, second channel circuit
There are three inputs, respectively y', z' and x, two output ends, respectively y and y', third channel circuit has the input to be
Y a, output end is z'；Three inputs of channel circuit interconnect with output end, constitute fractional order nonlinear
Chaos system circuit, the output end x of first passage circuit as second channel circuit input x, second channel circuit it is defeated
Go out to hold y as the input y of the first passage circuit and input y of third channel circuit, the output end y' of second channel circuit
Used as the input y' of second channel circuit, the output end z' of third channel circuit is used as the input z' of the first circuit passband and
The input z' of two channel circuits；
The equivalent mathematical model of the circuit is：
In formula, m1>0.89, m2>0.8, m3>0.91, k>0, x, y, z is the signal in nonlinear chaotic system circuit,It is x
M1Order derivative,It is the m of y2Order derivative,It is the m of z3Order derivative.
2. fractional order nonlinear chaos system circuit according to claim 1, it is characterised in that the first passage circuit
Including 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],
12 resistance [R12], the 13rd resistance [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], the first electric capacity [C1], the second electric capacity
[C2], the 3rd electric capacity [C3], the 4th electric capacity [C4], the 5th electric capacity [C5], the first multiplier [A1], the second multiplier [A2],
One operational amplifier [U1A], the second operational amplifier [U2A], the 3rd operational amplifier [U3A], four-operational amplifier [U4A]
With the 5th operational amplifier [U5A]；Two inputs of wherein the first multiplier [A1] for first passage circuit input y and
Input z', the input z' of first passage circuit is connected with an input of the second multiplier [A2], the first multiplier
The output end of [A1] is connected with another input of the second multiplier [A2], the output end and first resistor of the second multiplier [A2]
One end connection of [R1], the other end of first resistor [R1] is connected with the negative input end of the first operational amplifier [U1A], the first fortune
The positive input terminal for calculating amplifier [U1A] is connected to ground, the other end of first resistor [R1] one end simultaneously with second resistance [R2]
Connection, the other end of second resistance [R2] is connected with the output end of the first operational amplifier [U1A], second resistance [R2] it is another
End is connected with one end of 3rd resistor [R3] simultaneously, and the other end of 3rd resistor [R3] is connected with one end of the 4th resistance [R4],
The other end of 3rd resistor [R3] is connected with the negative input end of the second operational amplifier [U2A] simultaneously, the second operational amplifier
The positive input terminal of [U2A] is connected to ground, and the other end of the 4th resistance [R4] and the output end of the second operational amplifier [U2A] connect
Connect, the other end of the 4th resistance [R4] is connected with one end of the 5th resistance [R5] simultaneously, the other end of the 5th resistance [R5] and the
One end connection of six resistance [R6], the other end of the 5th resistance [R5] is connected with one end of the 8th resistance [R8] simultaneously, the 5th electricity
The other end for hindering [R5] be connected with one end of the first electric capacity [C1] simultaneously, the other end of the 5th resistance [R5] and meanwhile with the second electric capacity
One end connection of [C2], the other end of the 5th resistance [R5] is connected with one end of the 4th electric capacity [C4] simultaneously, the 5th resistance [R5]
The other end be connected with one end of the 5th electric capacity [C5] simultaneously, the other end of the 5th resistance [R5] at the same with the 3rd operational amplifier
The negative input end connection of [U3A], the positive input terminal of the 3rd operational amplifier [U3A] is connected to ground, the 6th resistance [R6] it is another
End is connected with one end of the 7th resistance [R7], and the other end of the 8th resistance [R8] is connected with one end of the 9th resistance [R9], and the 9th
The other end of resistance [R9] is connected with one end of the tenth resistance [R10], the other end and the 11st resistance of the tenth resistance [R10]
One end connection of [R11], the other end of the 11st resistance [R11] is connected with one end of the 12nd resistance [R12], the 12nd resistance
The other end of [R12] is connected with one end of the 13rd resistance [R13], and the other end of the 12nd resistance [R12] is simultaneously electric with first
Hold the other end connection of [C1], the other end of the 13rd resistance [R13] is connected with one end of the 14th resistance [R14], the 14th
The other end of resistance [R14] is connected with one end of the 15th resistance [R15], the other end and the 3rd electric capacity of the second electric capacity [C2]
One end connection of [C3], the other end of the 14th resistance [R14] is connected with the other end of the 3rd electric capacity [C3] simultaneously, the 4th electric capacity
The other end of [C4] is connected with the other end of the 5th electric capacity [C5], the other end and the 15th resistance [R15] of the 7th resistance [R7]
Other end connection, the other end of the 7th resistance [R7] is connected with the other end of the 4th electric capacity [C4] simultaneously, the 7th resistance [R7]
The other end be connected with the other end of the 5th electric capacity [C5] simultaneously, the other end of the 7th resistance [R7] at the same with the 3rd operation amplifier
The output end connection of device [U3A], the other end of the 7th resistance [R7] is connected with one end of the 16th resistance [R16] simultaneously, and the tenth
The other end of six resistance [R16] is connected with one end of the 17th resistance [R17], the other end of the 16th resistance [R16] simultaneously with
The negative input end connection of four-operational amplifier [U4A], the positive input terminal of four-operational amplifier [U4A] is connected to ground, and the tenth
The other end of seven resistance [R17] is connected with the output end of four-operational amplifier [U4A], four-operational amplifier [U4A] it is defeated
Go out end to be connected with one end of the 18th resistance [R18], the other end of the 18th resistance [R18] and the one of the 19th resistance [R19]
End connection, the other end of the 18th resistance [R18] is connected with the negative input end of the 5th operational amplifier [U5A], and the 5th computing is put
The positive input terminal of big device [U5A] is connected to ground, and the other end of the 19th resistance [R19] is defeated with the 5th operational amplifier [U5A]
Go out end connection, the output end of the 5th operational amplifier [U5A] as first passage circuit output end x.
3. fractional order nonlinear chaos system circuit according to claim 1, it is characterised in that the second channel circuit
Including the 20th resistance [R20], the 21st resistance [R21], the 22nd resistance [R22], the 23rd resistance [R23],
24 resistance [R24], the 25th resistance [R25], the 26th resistance [R26], the 27th [R27], the 28th electricity
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 electric capacity [C6], the 7th electric capacity [C7], the 8th electric capacity [C8], the 9th electric capacity [C9],
Tenth electric capacity [C10], the 11st electric capacity [C11], the 12nd electric capacity [C12], the 13rd electric capacity [C13], the 14th electric capacity
[C14], the 15th electric capacity [C15], the 3rd multiplier [A3], the 6th operational amplifier [U6A], the 7th operational amplifier [U7A],
8th operational amplifier [U8A], the 9th operational amplifier [U9A] and the tenth operational amplifier [U10A]；20th resistance [R20]
One end for second channel circuit input y', the other end of the 20th resistance [R20] and the one of the 21st resistance [R21]
End connection, the other end of the 20th resistance [R20] is connected with the negative input end of the 6th operational amplifier [U6A] simultaneously, the 6th fortune
The positive input terminal for calculating amplifier [U6A] is connected to ground, the other end and the 6th operational amplifier of the 21st resistance [R21]
The output end connection of [U6A], the other end of the 21st resistance [R21] is connected with one end of the 22nd resistance [R22] simultaneously,
The other end of the 22nd resistance [R22] is connected with one end of the 23rd resistance [R23], and two of the 3rd multiplier [A3] are defeated
Enter input z' and input x that end is respectively second channel circuit, the output end of the 3rd multiplier [A3] and the 24th electricity
One end connection of [R24] is hindered, the other end of the 24th resistance [R24] and the negative input end of the 7th operational amplifier [U7A] connect
Connect, the positive input terminal of the 7th operational amplifier [U7A] is connected to ground, the other end of the 24th resistance [R24] is simultaneously with second
One end connection of 15 resistance [R25], the output of the other end and the 7th operational amplifier [U7A] of the 25th resistance [R25]
End connection, the other end of the 25th resistance [R25] is connected with one end of the 26th resistance [R26] simultaneously, the 26th electricity
The other end for hindering [R26] is connected with the other end of the 23rd resistance [R23], and the other end of the 26th resistance [R26] is simultaneously
One end with the 27th resistance [R27] is connected, the other end of the 27th resistance [R27] and the 28th resistance [R28]
One end connects, and the other end of the 28th resistance [R28] is connected with one end of the 29th resistance [R29], the 29th resistance
The other end of [R29] is connected with one end of the 30th resistance [R30], the other end of the 30th resistance [R30] and the 31st electricity
One end connection of [R31] is hindered, the other end of the 31st resistance [R31] is connected with one end of the 32nd resistance [R32], the 3rd
The other end of 12 resistance [R32] is connected with one end of the 33rd resistance [R33], the other end of the 26th resistance [R26]
It is connected with one end of the 6th electric capacity [C6] simultaneously, the other end of the 6th electric capacity [C6] and the other end of the 29th resistance [R29]
Connection, the other end of the 26th resistance [R26] is connected with one end of the 7th electric capacity [C7] simultaneously, the 7th electric capacity [C7] it is another
End is connected with the other end of the 29th resistance [R29], the other end of the 26th resistance [R26] and meanwhile with the 8th electric capacity [C8]
One end connection, the other end of the 8th electric capacity [C8] is connected with the other end of the 29th resistance [R29], the 26th resistance
The other end of [R26] is connected with one end of the 9th electric capacity [C9] simultaneously, the other end and the 29th resistance of the 9th electric capacity [C9]
The other end connection of [R29], the other end of the 26th resistance [R26] is connected with one end of the tenth electric capacity [C10] simultaneously, and the tenth
The other end of electric capacity [C10] is connected with the other end of the 31st resistance [R31], and the other end of the 26th resistance [R26] is same
One end connection of the electric capacity of Shi Yu 11 [C11], the other end of the 11st electric capacity [C11] is another with the 31st resistance [R31]
One end connects, and the other end of the 26th resistance [R26] is connected with one end of the 12nd electric capacity [R12] simultaneously, the 12nd electric capacity
The other end of [R12] is connected with the other end of the 31st resistance [R31], the other end of the 26th resistance [R26] simultaneously with
One end connection of the 13rd electric capacity [C13], the other end of the 13rd electric capacity [C13] and the other end of the 33rd resistance [R33]
Connection, the other end of the 26th resistance [R26] is connected with one end of the 14th electric capacity [C14] simultaneously, the 14th electric capacity [C14]
The other end be connected with the other end of the 33rd resistance [R33], the other end of the 26th resistance [R26] is simultaneously with the 15th
One end connection of electric capacity [C15], the other end of the 15th electric capacity [C15] is connected with the other end of the 33rd resistance [R33], the
The other end of 26 resistance [R26] is connected with the negative input end of the 8th operational amplifier [U8A] simultaneously, the 8th operational amplifier
The positive input terminal of [U8A] is connected to ground, and the output end of the 8th operational amplifier [U8A] is another with the 33rd resistance [R33]
End connection, the output end of the 8th operational amplifier [U8A] as second channel circuit output end y', second channel circuit it is defeated
Go out to hold y' while be connected with one end of the 34th resistance [R34], the other end of the 34th resistance [R34] and the 35th electric
Hinder one end connection of [R35], the other end of the 34th resistance [R34] negative input simultaneously with the 9th operational amplifier [U9A]
End connection, the positive input terminal of the 9th operational amplifier [U9A] is connected to ground, the other end and the 9th of the 35th resistance [R35]
The output end connection of operational amplifier [U9A], the other end of the 35th resistance [R35] simultaneously with the 36th resistance [R36]
One end connection, the other end of the 36th resistance [R36] is connected with one end of the 37th resistance [R37], and the 36th is electric
The other end for hindering [R36] is connected with the negative input end of the tenth operational amplifier [U10A] simultaneously, the tenth operational amplifier [U10A]
Positive input terminal be connected to ground, the other end of the 37th resistance [R37] and the output end of the tenth operational amplifier [U10A]
Connection, the output end of the tenth operational amplifier [U10A] as second channel circuit output end y.
4. fractional order nonlinear chaos system circuit according to claim 1, it is characterised in that the third channel circuit
Including slide rheostat [R38], the 38th resistance [R39], the 39th resistance [R40], the 40th resistance [R41], the 4th
11 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 49th resistance
[R50], the 50th resistance [R51], the 51st resistance [R52], the 52nd resistance [R53], the 16th electric capacity [C16],
17 electric capacity [C17], the 18th electric capacity [C18], the 19th electric capacity [C19], the 20th electric capacity [C20], the 21st electric capacity
[C21], the 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]；One of slide rheostat [R38] is solid
Fixed end as third channel circuit input y, the anode of the sliding end of slide rheostat [R38] and the first diode [D1] connects
Connect, the negative terminal of the first diode [D1] is connected with the negative input end of the 11st operational amplifier [U11A], the 11st operation amplifier
The positive input terminal of device [U11A] is connected to ground, the negative terminal of the first diode [D1] one end simultaneously with the 38th resistance [R39]
Connection, the anode of the first diode [D1] is connected with the negative terminal of the second diode [D2] simultaneously, the 38th resistance [R39]
The other end is connected with the output end of the 11st operational amplifier [U11A], and the other end of the 38th resistance [R39] is simultaneously with the
One end connection of 39 resistance [R40], the other end of the 39th resistance [R40] and the anode of the second diode [D2] connect
Connect, the other end of the 39th resistance [R40] is connected with one end of the 40th resistance [R41] simultaneously, the 39th resistance [R40]
The other end simultaneously be connected with one end of the 41st resistance [R42], the other end and the 42nd of the 41st resistance [R42]
One end connection of resistance [R43], the other end of the 42nd resistance [R43] is connected with one end of the 43rd resistance [R44], the
The other end of 43 resistance [R44] is connected with one end of the 44th resistance [R45], the 44th resistance [R45] it is another
End is connected with one end of the 45th resistance [R46], the other end and the 46th resistance [R47] of the 45th resistance [R46]
One end connection, the other end of the 46th resistance [R47] is connected with one end of the 47th resistance [R48], and the 47th is electric
The other end for hindering [R48] is connected with one end of the 48th resistance [R49], the other end of the 39th resistance [R40] and meanwhile with
One end connection of the 16th electric capacity [C16], the other end of the 16th electric capacity [C16] is connected with one end of the 17th electric capacity [C17],
The other end of the 17th electric capacity [C17] is connected with the other end of the 45th resistance [R46], the 39th resistance [R40] it is another
One end is connected with one end of the 18th electric capacity [C18] simultaneously, the other end and the 19th electric capacity [C19] of the 18th electric capacity [C18]
One end connection, the other end of the 19th electric capacity [C19] is connected with the other end of the 47th resistance [R48], and the 39th is electric
The other end for hindering [R40] is connected with one end of the 20th electric capacity [C20] simultaneously, the other end and the 4th of the 20th electric capacity [C20]
The other end connection of 18 resistance [R49], the other end of the 39th resistance [R40] simultaneously with the 21st electric capacity [C21]
One end connects, and the other end of the 21st electric capacity [C21] is connected with the other end of the 48th resistance [R49], the 39th electricity
The other end for hindering [R40] is connected with the negative input end of the 12nd operational amplifier [U12A] simultaneously, the 12nd operational amplifier
[positive input terminal of U12A is connected to ground, and [output end of U12A is another with the 48th resistance [R49] for the 12nd operational amplifier
One end connects, and the other end of the 40th resistance [R41] is connected with the other end of the 48th resistance [R49], 40 resistance [R41]
The other end be connected with one end of the 49th resistance [R50] simultaneously, the other end of the 49th resistance [R50] and the 50th electric
One end connection of [R51] is hindered, the other end of the 49th resistance [R50] is simultaneously negative defeated with the 13rd operational amplifier [U13A]
Enter end connection, the positive input terminal of the 13rd operational amplifier [U13A] is connected to ground, the other end of 50 resistance [R51] and the
The output end connection of 13 operational amplifiers [U13A], the output end of the 13rd operational amplifier [U13A] is simultaneously with the 51st
One end connection of resistance [R52], the other end of the 51st resistance [R52] is connected with one end of the 52nd resistance [R53], the
The other end of 51 resistance [R52] is connected with the negative input end of the tenth four-operational amplifier [U14A] simultaneously, the 14th computing
The positive input terminal of amplifier [U14A] is connected to ground, and the other end of the 52nd resistance [R53] is used as the defeated of third channel circuit
Go out to hold z'.
5. the fractional order nonlinear chaos system circuit according to claim 2,3 or 4, it is characterised in that all of computing
The model all same of amplifier, its power supply is ± 15V dc sources.
6. the fractional order nonlinear chaos system circuit according to claim 2,3 or 4, it is characterised in that first resistor
[R1], 3rd resistor [R3], the 16th resistance [R16], the 17th resistance [R17], the 18th resistance [R18], the 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 resistance [R51] and the 52nd resistance [R53] are 10k Ω, second resistance [R2], the 4th resistance [R4],
25th resistance [R25], the 26th resistance [R26] and the 40th resistance [R41] are 100k Ω, and the 5th resistance [R5] is
500k Ω, 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 the 11st resistance [R11] is 15M Ω, and the 12nd resistance [R12] is
931k Ω, 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, the 37th resistance [R37] and the 5th
11 resistance [R52] are 50k Ω, and the 44th resistance [R45] is 9.1M Ω, and the 45th resistance [R46] is 732k Ω, the
46 resistance [R47] are 3.3M Ω, and the 47th resistance [R48] is 261k Ω, and the 48th resistance [R49] is 36.5k Ω,
The maximum value of slide rheostat [R38] be 200k Ω, the first electric capacity [C1], the 4th electric capacity [C4], the 15th electric capacity [C15],
18th electric capacity [C18], the 20th electric capacity [C20] are 0.22uF, and the second electric capacity [C2] and the 16th electric capacity [C16] are
0.33uF, the 3rd electric capacity [C3], the 5th electric capacity [C5] and the 21st electric capacity [C21] are 0.47uF, the 6th electric capacity [C6] and
Tenth electric capacity [C10] is 0.1uF, the 7th electric capacity [C7], the 8th electric capacity [C8], the 11st electric capacity [C11], the 12nd electric capacity
[C12], the 13rd electric capacity [C13] and the 14th electric capacity [C14] are 0.15uF, and the 9th electric capacity [C9] is 0.3uF, the 17th electricity
Hold [C17] and the 19th electric capacity [C19] is 1uF.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510848949.1A CN106817213B (en) | 2015-11-27 | 2015-11-27 | A kind of fractional order nonlinear chaos system circuit |
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|---|---|---|---|
| CN201510848949.1A CN106817213B (en) | 2015-11-27 | 2015-11-27 | A kind of fractional order nonlinear chaos system circuit |
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| CN106817213A true CN106817213A (en) | 2017-06-09 |
| CN106817213B CN106817213B (en) | 2019-08-09 |
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| CN108964871A (en) * | 2018-07-06 | 2018-12-07 | 烟台大学 | A kind of triple channel safe communication method based on double Chen's chaotic systems and terminal sliding mode |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107124263A (en) * | 2017-06-30 | 2017-09-01 | 湘潭大学 | Nested type multiscroll chaotic circuit |
| CN107124263B (en) * | 2017-06-30 | 2020-02-21 | 湘潭大学 | Nested multi-scroll chaotic circuit |
| CN108509704A (en) * | 2018-03-22 | 2018-09-07 | 武汉科技大学 | A kind of fractional order recalls the equivalent circuit of sensor |
| CN108365948A (en) * | 2018-03-30 | 2018-08-03 | 湘潭大学 | The memristor type hyperchaotic circuit of arbitrary even number and odd number scrollwork attractor can be generated |
| CN108964871A (en) * | 2018-07-06 | 2018-12-07 | 烟台大学 | A kind of triple channel safe communication method based on double Chen's chaotic systems and terminal sliding mode |
| CN108964871B (en) * | 2018-07-06 | 2021-01-26 | 烟台大学 | Three-channel safe communication method based on double-Chen chaotic system and terminal sliding mode |
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