CN109039581A - A kind of simple chaos system circuit of output Lorenz type switching attractor - Google Patents
A kind of simple chaos system circuit of output Lorenz type switching attractor Download PDFInfo
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- CN109039581A CN109039581A CN201811072958.6A CN201811072958A CN109039581A CN 109039581 A CN109039581 A CN 109039581A CN 201811072958 A CN201811072958 A CN 201811072958A CN 109039581 A CN109039581 A CN 109039581A
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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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- 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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Abstract
A kind of simple chaos system circuit with Lorenz type attractor is made of three road resistance, capacitor and operational amplifier LF347BN and multiplier AD633JN, resistance and operational amplifier LF347BN realize reverse phase addition and reverse phase operation, capacitor and operational amplifier LF347BN realize integral operation, and multiplication is realized by multiplier AD633JN；The invention proposes close proportionality coefficient with certain lotus root, the method for realizing active system and passive system overcomes the deficiencies of existing technologies, provide it is a kind of there is Lorenz type attractor chaos system, this for chaos control, synchronize etc. there is important job applications prospect.
Description
Technical field
Invention is related to the simple chaos system and circuit of a kind of output Lorenz type switching attractor, belongs to nonlinear circuit
System regions.
Background technique
Chaos research is explored from early stage to important breakthrough, and Journal of Sex Research heat in the world's is formed after 1970's
Tide, the field being related to include numerous subjects such as mathematics, physics, biology, meteorology, engineering science and economics, research
Achievement, more than add a new modern science subject branch, and almost permeate and affect the whole of modern science
A subject system.The research of Chaos is the new page of Development of Modern Science.Many scholars are known as chaology after quantum force
It learns and one of most influential scientific theory of twentieth century after the theory of relativity.Nonlinear science is that a research non-linear phenomena is total
Property basic science, the prospect with wide application realizes the invention proposes proportionality coefficient is closed with certain lotus root and is actively
The method of system and passive system overcomes the deficiencies of existing technologies, and provide one kind has Lorenz type attractor chaos system,
This for chaos control, synchronize etc. there is important job applications prospect.
Summary of the invention
1. a kind of simple chaos system circuit of output Lorenz type switching attractor, it is characterised in that:
(1) a kind of simple chaos system i of output Lorenz type switching attractor are as follows:
X in formula, y, z are state variable, and f (x) is function；
(2) whenWhen, system i becomes:
System ii has unique equalization point (- 1,1,1), is λ in the characteristic value of equalization point1=-1.325, λ2,3=0.6624
± 0.5623j, in characteristic value, real root is greater than 0, and the real part in compound radical is consequently belonging to saddle node less than 0, at this point, system have from
Swash chaos attractor；Circuit is designed according to system ii, circuit is by three road resistance, capacitor and operational amplifier LF347BN and multiplication
Device AD633JN composition, resistance and operational amplifier LF347BN realize reverse phase addition and reverse phase operation, capacitor and operational amplifier
LF347BN realizes integral operation, and multiplication is realized that switching circuit is by resistance, operational amplifier LF347BN by multiplier AD633JN
It is formed with selector ADG409BR, resistance and operational amplifier LF347BN realize comparator, and data are selected by selector
ADG409BR (S1) is realized；
The reverse phase adding input of the first via connects the integral output on the first via and the second tunnel；Multiplier (A1) input connects respectively
The anti-phase output of the first via and the anti-phase output on third road, the output of multiplier (A1) connect the reverse phase addition input on the second tunnel, the
The input of two tunnel reverse phase adders meets function f (x), and the input of multiplier (A2) connects anti-phase output and the second tunnel of the first via respectively
Anti-phase output, the output of multiplier (A2) connect third road reverse phase addition input, third road reverse phase addition input by -1V it is straight
Flow power ground；
Realize that the positive input terminal of the operational amplifier LF347BN (U3B) of comparator function connects above-mentioned third in switching circuit
The integral output end on road, the negative input end ground connection of operational amplifier LF347BN (U3B), operational amplifier LF347BN's (U3B)
Output end connects the 1st pin of selector ADG409BR (S1), the output end of operational amplifier LF347BN (U3B) by resistance R19
It is grounded by resistance R19 and resistance R20；The 2nd pin of selector ADG409BR (S1) meets VCC；Selector ADG409BR (S1)
The 3rd pin meet VEE；The 4th pin of selector ADG409BR (S1) connects the reversed-phase output of the above-mentioned first via, selector
The 5th pin of ADG409BR (S1) connects the reversed-phase output on above-mentioned second tunnel, selector ADG409BR (S1) the 6th, 7,9,10,
11,12,13 pin floating；The 8th pin of selector ADG409BR (S1) connects the reverse phase adding input on above-mentioned second tunnel, selection
The 14th pin of device ADG409BR (S1) meets VCC, the 15th pin ground connection of selector ADG409BR (S1), selector ADG409BR
(S1) the 16th pin ground connection.
When f (x) connects switching function output, circuit realizes the system ii with self-excitation chaos attractor.
The utility model has the advantages that realizing the side of active system and passive system the invention proposes proportionality coefficient is closed with certain lotus root
Method overcomes the deficiencies of existing technologies, provide it is a kind of there is Lorenz type attractor chaos system, this for chaos control,
Synchronizing etc. has important job applications prospect, enriches the type of chaos system, mentions for chaos system applied to engineering practice
More more options are supplied.
Detailed description of the invention
Fig. 1 is the circuit diagram of realization system.
Fig. 2 is the phasor of system ii.
Fig. 3 is the circuit diagram of realization system switching
Specific embodiment
The present invention is further described in detail with preferred embodiment with reference to the accompanying drawing, referring to figures 1-3.
1. a kind of simple chaos system circuit of output Lorenz type switching attractor, it is characterised in that:
(1) a kind of simple chaos system i of output Lorenz type switching attractor are as follows:
X in formula, y, z are state variable, and f (x) is function；
(2) whenWhen, system i becomes:
System ii has unique equalization point (- 1,1,1), is λ in the characteristic value of equalization point1=-1.325, λ2,3=0.6624
± 0.5623j, in characteristic value, real root is greater than 0, and the real part in compound radical is consequently belonging to saddle node less than 0, at this point, system have from
Swash chaos attractor；Circuit is designed according to system ii, circuit is by three road resistance, capacitor and operational amplifier LF347BN and multiplication
Device AD633JN composition, resistance and operational amplifier LF347BN realize reverse phase addition and reverse phase operation, capacitor and operational amplifier
LF347BN realizes integral operation, and multiplication is realized that switching circuit is by resistance, operational amplifier LF347BN by multiplier AD633JN
It is formed with selector ADG409BR, resistance and operational amplifier LF347BN realize comparator, and data are selected by selector
ADG409BR (S1) is realized；
The reverse phase adding input of the first via connects the integral output on the first via and the second tunnel；Multiplier (A1) input connects respectively
The anti-phase output of the first via and the anti-phase output on third road, the output of multiplier (A1) connect the reverse phase addition input on the second tunnel, the
The input of two tunnel reverse phase adders meets function f (x), and the input of multiplier (A2) connects anti-phase output and the second tunnel of the first via respectively
Anti-phase output, the output of multiplier (A2) connect third road reverse phase addition input, third road reverse phase addition input by -1V it is straight
Flow power ground；
Realize that the positive input terminal of the operational amplifier LF347BN (U3B) of comparator function connects above-mentioned third in switching circuit
The integral output end on road, the negative input end ground connection of operational amplifier LF347BN (U3B), operational amplifier LF347BN's (U3B)
Output end connects the 1st pin of selector ADG409BR (S1), the output end of operational amplifier LF347BN (U3B) by resistance R19
It is grounded by resistance R19 and resistance R20；The 2nd pin of selector ADG409BR (S1) meets VCC；Selector ADG409BR (S1)
The 3rd pin meet VEE；The 4th pin of selector ADG409BR (S1) connects the reversed-phase output of the above-mentioned first via, selector
The 5th pin of ADG409BR (S1) connects the reversed-phase output on above-mentioned second tunnel, selector ADG409BR (S1) the 6th, 7,9,10,
11,12,13 pin floating；The 8th pin of selector ADG409BR (S1) connects the reverse phase adding input on above-mentioned second tunnel, selection
The 14th pin of device ADG409BR (S1) meets VCC, the 15th pin ground connection of selector ADG409BR (S1), selector ADG409BR
(S1) the 16th pin ground connection.
When f (x) connects switching function output, circuit realizes the system ii with self-excitation chaos attractor.
Certainly, above description is not limitation to invention, and the present invention is also not limited to the example above, the art it is general
The variations, modifications, additions or substitutions that logical technical staff is made within the essential scope of the present invention also belong to protection of the invention
Range.
Claims (1)
1. a kind of simple chaos system circuit of output Lorenz type switching attractor, it is characterised in that:
(1) a kind of simple chaos system i of output Lorenz type switching attractor are as follows:
X in formula, y, z are state variable, and f (x) is function；
(2) whenWhen, system i becomes:
System ii has unique equalization point (- 1,1,1), is λ in the characteristic value of equalization point1=-1.325, λ2,3=0.6624 ±
0.5623j, in characteristic value, real root is greater than 0, and the real part in compound radical is consequently belonging to saddle node less than 0, at this point, system has self-excitation
Chaos attractor；Circuit is designed according to system ii, circuit is by three road resistance, capacitor and operational amplifier LF347BN and multiplier
AD633JN composition, resistance and operational amplifier LF347BN realize reverse phase addition and reverse phase operation, capacitor and operational amplifier
LF347BN realizes integral operation, and multiplication is realized that switching circuit is by resistance, operational amplifier LF347BN by multiplier AD633JN
It is formed with selector ADG409BR, resistance and operational amplifier LF347BN realize comparator, and data are selected by selector
ADG409BR (S1) is realized；
The reverse phase adding input of the first via connects the integral output on the first via and the second tunnel；Multiplier (A1) input connects first respectively
The anti-phase output on road and the anti-phase output on third road, the output of multiplier (A1) connect the reverse phase addition input on the second tunnel, the second tunnel
The input of reverse phase adder meets function f (x), the input of multiplier (A2) connect respectively the first via anti-phase output and the second tunnel it is anti-
It mutually exports, the output of multiplier (A2) connects the reverse phase addition input on third road, and reverse phase addition input in third road passes through -1V direct current
Source ground connection；
Realize that the positive input terminal of the operational amplifier LF347BN (U3B) of comparator function connects above-mentioned third road in switching circuit
Integrate output end, the negative input end ground connection of operational amplifier LF347BN (U3B), the output of operational amplifier LF347BN (U3B)
End connects the 1st pin of selector ADG409BR (S1) by resistance R19, and the output end of operational amplifier LF347BN (U3B) passes through
Resistance R19 and resistance R20 ground connection；The 2nd pin of selector ADG409BR (S1) meets VCC；The 3rd of selector ADG409BR (S1)
Pin meets VEE；The 4th pin of selector ADG409BR (S1) meets the reversed-phase output of the above-mentioned first via, selector ADG409BR
(S1) the 5th pin connects the reversed-phase output on above-mentioned second tunnel, selector ADG409BR (S1) the 6th, 7,9,10,11,12,13
Pin floating；The 8th pin of selector ADG409BR (S1) connects the reverse phase adding input on above-mentioned second tunnel, selector
The 14th pin of ADG409BR (S1) meets VCC, the 15th pin ground connection of selector ADG409BR (S1), selector ADG409BR
(S1) the 16th pin ground connection.
When f (x) connects switching function output, circuit realizes the system ii with self-excitation chaos attractor.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
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| CN201811072958.6A CN109039581A (en) | 2016-04-28 | 2016-04-28 | A kind of simple chaos system circuit of output Lorenz type switching attractor |
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| CN201610278609.4A CN105790924B (en) | 2016-04-28 | 2016-04-28 | A kind of simple chaos system circuit with Lorenz type attractors |
| CN201811072958.6A CN109039581A (en) | 2016-04-28 | 2016-04-28 | A kind of simple chaos system circuit of output Lorenz type switching attractor |
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| CN201811072958.6A Pending CN109039581A (en) | 2016-04-28 | 2016-04-28 | A kind of simple chaos system circuit of output Lorenz type switching attractor |
| CN201610278609.4A Active CN105790924B (en) | 2016-04-28 | 2016-04-28 | A kind of simple chaos system circuit with Lorenz type attractors |
| CN201811072942.5A Pending CN109039579A (en) | 2016-04-28 | 2016-04-28 | A kind of simple chaos system circuit of Lorenz type attractor |
| CN201811072944.4A Pending CN109039580A (en) | 2016-04-28 | 2016-04-28 | A kind of simple chaos system circuit generating Lorenz type attractor |
| CN201811073292.6A Pending CN109039582A (en) | 2016-04-28 | 2016-04-28 | A kind of simple chaos system circuit exporting Lorenz type attractor |
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| CN201811072942.5A Pending CN109039579A (en) | 2016-04-28 | 2016-04-28 | A kind of simple chaos system circuit of Lorenz type attractor |
| CN201811072944.4A Pending CN109039580A (en) | 2016-04-28 | 2016-04-28 | A kind of simple chaos system circuit generating Lorenz type attractor |
| CN201811073292.6A Pending CN109039582A (en) | 2016-04-28 | 2016-04-28 | A kind of simple chaos system circuit exporting Lorenz type attractor |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112152774A (en) * | 2019-06-28 | 2020-12-29 | 天津科技大学 | non-Hamilton system capable of generating four-scroll chaotic current and circuit implementation thereof |
| CN112422258A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | Improved Sprott-A system with single cluster of conservative chaotic streams and circuit implementation of improved Sprott-A system |
| CN112422260A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | non-Hamilton system with three-dimensional 2 x 2 cluster conservative chaotic stream and circuit implementation thereof |
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| CN108337081B (en) * | 2018-03-21 | 2019-09-17 | 齐鲁理工学院 | One kind containing constant term three-dimensional chaos circuit three times |
| CN109474416B (en) * | 2018-12-29 | 2020-09-29 | 安顺学院 | Hyperchaotic signal generating circuit with hidden attractor |
| CN111538245B (en) * | 2020-06-26 | 2022-06-03 | 西京学院 | Robust control method of chaotic system with hidden attractor |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112152774A (en) * | 2019-06-28 | 2020-12-29 | 天津科技大学 | non-Hamilton system capable of generating four-scroll chaotic current and circuit implementation thereof |
| CN112152774B (en) * | 2019-06-28 | 2022-08-02 | 天津科技大学 | Construction method of non-Hamilton system capable of generating four-scroll chaotic stream |
| CN112422258A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | Improved Sprott-A system with single cluster of conservative chaotic streams and circuit implementation of improved Sprott-A system |
| CN112422260A (en) * | 2019-08-23 | 2021-02-26 | 天津科技大学 | non-Hamilton system with three-dimensional 2 x 2 cluster conservative chaotic stream and circuit implementation thereof |
| CN112422258B (en) * | 2019-08-23 | 2022-07-29 | 天津科技大学 | Construction method of improved Sprott-A system with single cluster of conservative chaotic streams |
| CN112422260B (en) * | 2019-08-23 | 2022-08-02 | 天津科技大学 | Construction method of non-Hamilton system with three-dimensional 2 x 2 cluster conservative chaotic stream |
Also Published As
| Publication number | Publication date |
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| CN109039579A (en) | 2018-12-18 |
| CN109039582A (en) | 2018-12-18 |
| CN105790924A (en) | 2016-07-20 |
| CN105790924B (en) | 2018-11-02 |
| CN109039580A (en) | 2018-12-18 |
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