CN105871534B - A kind of chaos system circuit for producing 1-4 wing attractors - Google Patents

A kind of chaos system circuit for producing 1-4 wing attractors Download PDF

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CN105871534B
CN105871534B CN201610183491.7A CN201610183491A CN105871534B CN 105871534 B CN105871534 B CN 105871534B CN 201610183491 A CN201610183491 A CN 201610183491A CN 105871534 B CN105871534 B CN 105871534B
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resistance
multiplier
adder
tunnel
operational amplifier
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CN105871534A (en
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杨高林
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Jiaxing Zhixu Information Technology Co.,Ltd.
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Qingdao Huaren Technology Incubator Co Ltd
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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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/12—Details relating to cryptographic hardware or logic circuitry

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  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Feedback Control In General (AREA)

Abstract

It is a kind of produce 14 wing attractors chaos system be：X in formula, y, z are state variable, and d is systematic parameter；As d=2, system i produces the attractor of single-blade；As d=3, system i produces the attractor of double-vane；As d=3.6, system i produces the attractor of three wings；As d=5, system i produces the attractor of four wings；The analog circuit being made of according to system design resistance, capacitance, operational amplifier and multiplier, resistance, capacitance and operational amplifier realize addition, integration and anti-phase computing, multiplier realizes multiplying, and the multiplier uses AD633JN, and the operational amplifier uses LF347N.

Description

A kind of chaos system circuit for producing 1-4 wing attractors
Technical field
The present invention relates to a kind of chaos system circuit for producing 1-4 wing attractors, belong to electronic information field.
Background technology
At present, the chaos system that oneself has such as Loren systems, Chen systems and Lu systems etc. can produce double-wing chaotic attractor, On the basis of oneself has chaos system, the attraction of four wings can be produced by increasing nonlinear terms or changing the method for multiple parameters Son, but only change that a parameter can produce single-blade, double-vane, three wings and four wings are inhaled the chaos system of son and are not suggested also, The present invention is the defects of overcoming the prior art, there is provided in the case that one kind can be by only changing a parameter, generation single-blade, The chaos system and circuit of double-vane, three wings and four-winged chaotic attractor, this is controlled, synchronously and in communication engineering etc. for chaos Be of great significance using tool.
The content of the invention
The technical problem to be solved in the present invention is to provide a kind of chaos system circuit for producing 1-4 wing attractors：
A kind of 1. chaos system circuit for producing 1-4 wing attractors, it is characterised in that：
The chaos system i that 1-4 wing attractors can be produced is：
X in formula, y, z are state variable, and d is systematic parameter；As d=2, system i produces the attractor of single-blade；Work as d=3 When, system i produces the attractor of double-vane；As d=3.6, system i produces the attractor of three wings；As d=5, system i is produced The attractor of four wings；
The analog circuit being made of according to system i designs resistance, capacitance, operational amplifier and multiplier, resistance R2And R4With Operational amplifier U4A realizes first via adder, resistance R5, capacitance C1 and operational amplifier U4B realize first via integrator, electricity Hinder R6、R7First via phase inverter is realized with operational amplifier U4C；Resistance R1、R3、R8、R9And R10Is realized with operational amplifier U4D Two tunnel adders, resistance R11, capacitance C2 and operational amplifier U5A realize the second road integrator, resistance R20、R21And operation amplifier Device U2D realizes No. second phase inverter；Resistance R12、R13、R18And R14The 3rd tunnel adder, resistance are realized with operational amplifier U5B R15, capacitance C3 and operational amplifier U5C realize the 3rd road integrator, resistance R16、R17The 3rd tunnel is realized with operational amplifier U5D Phase inverter；Multiplier realizes multiplying, and the multiplier uses AD633JN, and the operational amplifier uses LF347N；
Circuit system is by first via adder, integrator and phase inverter, the second tunnel adder, integrator and phase inverter and Three tunnel adders, integrator and phase inverter composition, the input terminal of first via adder pass through resistance R2Connect the second road integrator Output terminal, the input terminal of the second tunnel adder pass through resistance R9Connect the output terminal of first via phase inverter, the second tunnel adder it is defeated Enter end and pass through resistance R1Connect the output terminal of the second road integrator；Multiplier A3 input termination No. second phase inverter output terminal and The output terminal of 3rd road integrator, an input terminal of the output termination multiplier A1 of multiplier A3 and one of multiplier A2 it is defeated Enter end, the output terminal of another input the 3rd road integrator of termination of multiplier A1, the output terminal of multiplier A1 passes through resistance R3 Meet the input terminal of the second tunnel adder, the output terminal of another input termination No. second phase inverter of multiplier A2, multiplier A2 Output terminal pass through resistance R13The input terminal of the 3rd tunnel adder is connect, the input terminal of multiplier A4 connects the second road integrator respectively The output terminal of output terminal and the 3rd road integrator, the output terminal of multiplier A4 pass through resistance R8Connect the input of the second tunnel adder End；3rd tunnel adder passes through resistance R18The output terminal of No. second phase inverter is connect, passes through resistance R12Connect the defeated of No. threeth phase inverter Outlet；
As resistance R1During=50k Ω, corresponding parameter d=2, circuit produces the attractor of single-blade；As resistance R1During=30k Ω, Corresponding parameter d=3, circuit produce the attractor of double-vane；As resistance R1During=28k Ω, corresponding parameter d=3, circuit produces three wings Attractor；As resistance R1During=20k Ω, corresponding parameter d=3.6, circuit produces the attractor of four wings.
Beneficial effect：In the case of can be by only changing a parameter the present invention provides one kind, single-blade, double be produced The chaos system and circuit of the wing, three wings and four-winged chaotic attractor, enrich the type of chaos system, are applied to communication for chaos system The practices such as engineering tool is of great significance.
Brief description of the drawings
Fig. 1 is the schematic diagram of circuit connection structure of the preferred embodiment of the present invention.
Fig. 2 is single-blade attractor phasor.Fig. 3 is double-wing chaotic attractor phasor.Fig. 4 is three wings attractor phasor.Fig. 5 is four wings Attractor phasor.
Embodiment
The present invention is further described in detail with preferred embodiment below in conjunction with the accompanying drawings, referring to Fig. 1-Fig. 5.
A kind of 1. chaos system circuit for producing 1-4 wing attractors, it is characterised in that：
The chaos system i that 1-4 wing attractors can be produced is：
X in formula, y, z are state variable, and d is systematic parameter；As d=2, system i produces the attractor of single-blade；Work as d=3 When, system i produces the attractor of double-vane；As d=3.6, system i produces the attractor of three wings；As d=5, system i is produced The attractor of four wings；
The analog circuit being made of according to system i designs resistance, capacitance, operational amplifier and multiplier, resistance R2And R4With Operational amplifier U4A realizes first via adder, resistance R5, capacitance C1 and operational amplifier U4B realize first via integrator, electricity Hinder R6、R7First via phase inverter is realized with operational amplifier U4C；Resistance R1、R3、R8、R9And R10Is realized with operational amplifier U4D Two tunnel adders, resistance R11, capacitance C2 and operational amplifier U5A realize the second road integrator, resistance R20、R21And operation amplifier Device U2D realizes No. second phase inverter；Resistance R12、R13、R18And R14The 3rd tunnel adder, resistance are realized with operational amplifier U5B R15, capacitance C3 and operational amplifier U5C realize the 3rd road integrator, resistance R16、R17The 3rd tunnel is realized with operational amplifier U5D Phase inverter；Multiplier realizes multiplying, and the multiplier uses AD633JN, and the operational amplifier uses LF347N；
Circuit system is by first via adder, integrator and phase inverter, the second tunnel adder, integrator and phase inverter and Three tunnel adders, integrator and phase inverter composition, the input terminal of first via adder pass through resistance R2Connect the second road integrator Output terminal, the input terminal of the second tunnel adder pass through resistance R9Connect the output terminal of first via phase inverter, the second tunnel adder it is defeated Enter end and pass through resistance R1Connect the output terminal of the second road integrator；Multiplier A3 input termination No. second phase inverter output terminal and The output terminal of 3rd road integrator, an input terminal of the output termination multiplier A1 of multiplier A3 and one of multiplier A2 it is defeated Enter end, the output terminal of another input the 3rd road integrator of termination of multiplier A1, the output terminal of multiplier A1 passes through resistance R3 Meet the input terminal of the second tunnel adder, the output terminal of another input termination No. second phase inverter of multiplier A2, multiplier A2 Output terminal pass through resistance R13The input terminal of the 3rd tunnel adder is connect, the input terminal of multiplier A4 connects the second road integrator respectively The output terminal of output terminal and the 3rd road integrator, the output terminal of multiplier A4 pass through resistance R8Connect the input of the second tunnel adder End；3rd tunnel adder passes through resistance R18The output terminal of No. second phase inverter is connect, passes through resistance R12Connect the defeated of No. threeth phase inverter Outlet；
As resistance R1During=50k Ω, corresponding parameter d=2, circuit produces the attractor of single-blade；As resistance R1During=30k Ω, Corresponding parameter d=3, circuit produce the attractor of double-vane；As resistance R1During=28k Ω, corresponding parameter d=3, circuit produces three wings Attractor；As resistance R1During=20k Ω, corresponding parameter d=3.6, circuit produces the attractor of four wings.
Certainly, described above is not limitation to invention, and the present invention is also not limited to the example above, the art it is general The variations, modifications, additions or substitutions that logical technical staff is made in the essential scope of the present invention, fall within the protection of the present invention Scope.

Claims (1)

  1. A kind of 1. chaos system circuit for producing 1-4 wing attractors, it is characterised in that：
    The chaos system i that 1-4 wing attractors can be produced is：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>d</mi> <mi>x</mi> <mo>/</mo> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mi>y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>d</mi> <mi>y</mi> <mo>/</mo> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <mi>x</mi> <mo>-</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> <mo>-</mo> <mi>z</mi> <mo>-</mo> <mi>d</mi> <mo>)</mo> </mrow> <mi>y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>d</mi> <mi>z</mi> <mo>/</mo> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>z</mi> <mo>-</mo> <mi>y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>i</mi> </mrow>
    X in formula, y, z are state variable, and d is systematic parameter；As d=2, system i produces the attractor of single-blade；As d=3, System i produces the attractor of double-vane；As d=3.6, system i produces the attractor of three wings；As d=5, system i produces four wings Attractor；
    The analog circuit being made of according to system i designs resistance, capacitance, operational amplifier and multiplier, resistance R2And R4And computing Amplifier U4A realizes first via adder, resistance R5, capacitance C1 and operational amplifier U4B realize first via integrator, resistance R6、 R7First via phase inverter is realized with operational amplifier U4C；Resistance R1、R3、R8、R9And R10The second tunnel is realized with operational amplifier U4D Adder, resistance R11, capacitance C2 and operational amplifier U5A realize the second road integrator, resistance R20、R21With operational amplifier U2D Realize No. second phase inverter；Resistance R12、R13、R18And R14The 3rd tunnel adder, resistance R are realized with operational amplifier U5B15, electricity Hold C3 and operational amplifier U5C and realize the 3rd road integrator, resistance R16、R17Realize that the 3rd tunnel is anti-phase with operational amplifier U5D Device；Multiplier realizes multiplying, and the multiplier uses AD633JN, and the operational amplifier uses LF347N；
    Circuit system is by first via adder, integrator and phase inverter, the second tunnel adder, integrator and phase inverter and the 3rd tunnel Adder, integrator and phase inverter composition, the input terminal of first via adder pass through resistance R2Connect the output of the second road integrator End, the input terminal of the second tunnel adder pass through resistance R9Connect the output terminal of first via phase inverter, the input terminal of the second tunnel adder Pass through resistance R1Connect the output terminal of the second road integrator；The output terminal and the 3rd of input termination No. second phase inverter of multiplier A3 The output terminal of road integrator, an input of an input terminal and multiplier A2 of the output termination multiplier A1 of multiplier A3 End, the output terminal of another input the 3rd road integrator of termination of multiplier A1, the output terminal of multiplier A1 pass through resistance R3Connect The input terminal of second tunnel adder, the output terminal of another input termination No. second phase inverter of multiplier A2, multiplier A2's Output terminal passes through resistance R13The input terminal of the 3rd tunnel adder is connect, the input terminal of multiplier A4 connects the defeated of the second road integrator respectively The output terminal of outlet and the 3rd road integrator, the output terminal of multiplier A4 pass through resistance R8Connect the input terminal of the second tunnel adder； 3rd tunnel adder passes through resistance R18The output terminal of No. second phase inverter is connect, passes through resistance R12Connect the output of No. threeth phase inverter End；
    As resistance R1During=50k Ω, corresponding parameter d=2, circuit produces the attractor of single-blade；As resistance R1It is corresponding during=30k Ω Parameter d=3, circuit produce the attractor of double-vane；As resistance R1During=28k Ω, corresponding parameter d=3, circuit produces the suction of three wings Introduction；As resistance R1During=20k Ω, corresponding parameter d=3.6, circuit produces the attractor of four wings.
CN201610183491.7A 2016-03-28 2016-03-28 A kind of chaos system circuit for producing 1-4 wing attractors Active CN105871534B (en)

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* Cited by examiner, † Cited by third party
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CN102611388A (en) * 2012-03-26 2012-07-25 常州大学 One-parameter robust chaotic signal source
CN103414551A (en) * 2013-08-02 2013-11-27 南京师范大学 Three-dimensional four-winged chaotic circuit

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102611388A (en) * 2012-03-26 2012-07-25 常州大学 One-parameter robust chaotic signal source
CN103414551A (en) * 2013-08-02 2013-11-27 南京师范大学 Three-dimensional four-winged chaotic circuit

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