CN103227714A - Three-dimensional multi-wing chaotic system - Google Patents
Three-dimensional multi-wing chaotic system Download PDFInfo
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- CN103227714A CN103227714A CN2013101449530A CN201310144953A CN103227714A CN 103227714 A CN103227714 A CN 103227714A CN 2013101449530 A CN2013101449530 A CN 2013101449530A CN 201310144953 A CN201310144953 A CN 201310144953A CN 103227714 A CN103227714 A CN 103227714A
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Abstract
The invention relates to a three-dimensional multi-wing chaotic system, and provides a method for generating multi-wing butterfly-shaped chaotic attractors. The improved three-dimensional multi-wing chaotic system is constructed by adding a break sign linear function and based on a three-dimensional lorentz chaotic system. The multi-wing butterfly-shaped chaotic attractors can be obtained by setting different sign function values; the feasibility and the validation of the method are verified by an experimental result; and the three-dimensional multi-wing chaotic system has a wide application prospect and an important application value in the fields of radars, secret communication, electronic countermeasures and the like.
Description
Technical field
The present invention relates to a kind of three-dimensional multiple wing three-dimensional chaos system, belong to electronic communication field.
Background technology
Since Lorenz in 1963 proposed first chaotic model, people had produced great interest to the chaos phenomenon in the non linear system.2002,
Find unified chaotic system.2003, Liu etc. constructed one four wing chaos system, had caused that but people are to constructing the interest of four wings and multiple wing chaos system.But for the structure of multiple wing chaos system, study also less, and for the structure such chaos system still challenging.
This paper by increasing a break sign linear function, proposes a kind of improved three-dimensional multiple wing chaos system on the basis of a class Lorentz chaos system, this system can produce the butterfly-like chaos attractor of multiple wing by certain parameter is set.Experiment show the feasibility and the validity of this method; To have a wide range of applications in fields such as radar, secure communication, electronic countermeasuress and important use value.
Summary of the invention
Technical problem to be solved by this invention provides a kind of improved three-dimensional multiple wing chaos system, and this system can produce the butterfly-like chaos attractor of multiple wing by certain parameter is set.
In order to solve the problems of the technologies described above, on the basis of a class Lorentz chaos system, the invention provides a kind of improved three-dimensional multiple wing chaos system, by different parameters is set, this system can produce the butterfly-like chaos attractor of multiple wing.The quantic of the chaos system of this method construct is simple, and this system has bigger using value on engineering, especially the application in secure communication.
The pairing partial differential equation of described three-dimensional class Lorentz chaos system are:
(1)
Wherein, work as parameter
The time, system shows as class Lorentz chaos system, wherein
,
,
Be state variable.
Equation (1) is carried out conversion, put in order then, can obtain partial differential is equation:
(2)
Wherein, function
For:
Work as parameter
When getting different numerical value respectively, can obtain the butterfly-like chaos attractor of dissimilar multiple wings.
Effect of the present invention and effect
(1) the present invention has realized providing a kind of improved three-dimensional multiple wing chaos system, works as parameter
When getting different numerical value respectively, can obtain the dissimilar butterfly-like chaos attractors of unified multiple wing.
(2) adopt improved three-dimensional multiple wing chaos system of the present invention, its output signal has bigger dynamic range, and this chaos signal source has the wideband section characteristic of different frequency range scope, indicates that it is at radar, secure communication, fields such as the electronic countermeasures value that has a wide range of applications.
Description of drawings
For the easier quilt of content of the present invention is clearly understood, below the specific embodiment and in conjunction with the accompanying drawings of basis, the present invention is further detailed explanation.
The butterfly-like chaos attractor two dimension of 2 wing chaos phasor that Fig. 1 is produced for three-dimensional class Lorentz chaos system (1).
Fig. 2 is that improved three-dimensional multiple wing chaos system (2) produces the butterfly-like chaos attractor two dimension of 4 wing chaos phasor.
Fig. 3 is that improved three-dimensional multiple wing chaos system (2) produces the butterfly-like chaos attractor two dimension of 6 wing chaos phasor.
Fig. 4 is that improved three-dimensional multiple wing chaos system (2) produces the butterfly-like chaos attractor two dimension of 10 wing chaos phasor.
Embodiment
The pairing partial differential equation of described three-dimensional class Lorentz chaos system are:
Wherein, work as parameter
The time, system shows as class Lorentz chaos system, its both wings chaos attractor as shown in Figure 1, wherein
,
,
Be state variable.
Equation (1) is carried out conversion, put in order then, can obtain partial differential is equation:
Wherein, function
For:
Work as parameter
When getting different numerical value respectively, can obtain the butterfly-like chaos attractor of dissimilar multiple wings.For improved three-dimensional multiple wing chaos system (2), the writ state variable (
); Work as parameter
;
The time, the butterfly-like chaos attractor of its 4 wing is as shown in Figure 2; Other parameter constant, when
The time, the butterfly-like chaos attractor of its 6 wing is as shown in Figure 3; Work as parameter
The time, the butterfly-like chaos attractor of its 10 wing is as shown in Figure 4; From Fig. 2, Fig. 3 and Fig. 4 as can be seen, above-mentioned three-dimensional multiple wing chaos system is in parameter
When getting different numerical value respectively, can obtain the butterfly-like chaos attractor of dissimilar multiple wings.
The foregoing description only is for example of the present invention clearly is described, and be not to be qualification to embodiments of the present invention, for those of ordinary skill in the field, can also make other changes in different forms on the basis of the above description.
Claims (3)
1. three-dimensional multiple wing chaos system, its feature comprises: on the basis of a class Lorentz chaos system, the present invention proposes a kind of improved three-dimensional chaos system, by different parameters is set, this system can produce the butterfly-like chaos attractor of multiple wing; The quantic of the unified multiple wing chaos system of this method construct is simple, and this system has bigger using value on engineering, especially the application in secure communication.
2. a kind of three-dimensional multiple wing chaos system according to claim 1 is characterized in that, the pairing partial differential equation of described three-dimensional class Lorentz chaos system are:
Wherein, work as parameter
The time, system shows as class Lorentz chaos system, wherein
,
,
Be state variable.
3. three-dimensional multiple wing chaos system according to claim 1 is characterized in that: equation (1) is carried out conversion, put in order then, can obtain partial differential is equation:
Wherein, function
For:
Work as parameter
When getting different numerical value respectively, can obtain the butterfly-like chaos attractor of dissimilar multiple wings.
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| CN2013101449530A CN103227714A (en) | 2013-04-25 | 2013-04-25 | Three-dimensional multi-wing chaotic system |
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5291555A (en) * | 1992-12-14 | 1994-03-01 | Massachusetts Institute Of Technology | Communication using synchronized chaotic systems |
| CN102916802A (en) * | 2012-09-27 | 2013-02-06 | 滨州学院 | Fractional-order automatic switching chaotic system method for four Lorenz type systems and analog circuit |
| CN102957531A (en) * | 2012-10-29 | 2013-03-06 | 滨州学院 | Method for realizing automatic switching of seven Lorenz type chaotic systems and analog circuit |
-
2013
- 2013-04-25 CN CN2013101449530A patent/CN103227714A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5291555A (en) * | 1992-12-14 | 1994-03-01 | Massachusetts Institute Of Technology | Communication using synchronized chaotic systems |
| CN102916802A (en) * | 2012-09-27 | 2013-02-06 | 滨州学院 | Fractional-order automatic switching chaotic system method for four Lorenz type systems and analog circuit |
| CN102957531A (en) * | 2012-10-29 | 2013-03-06 | 滨州学院 | Method for realizing automatic switching of seven Lorenz type chaotic systems and analog circuit |
Non-Patent Citations (3)
| Title |
|---|
| 包伯成: "混沌动力学系统延拓与分析", 《中国博士学位论文全文数据库(基础科学辑)》 * |
| 朱从旭，孙克辉: "基于新型类洛伦兹吸引子的混沌同步保密通信系统", 《山东大学学报(理学版)》 * |
| 朱从旭，孙克辉: "基于新型类洛伦兹吸引子的混沌同步保密通信系统", 《山东大学学报(理学版)》, vol. 46, no. 9, 30 September 2011 (2011-09-30) * |
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Application publication date: 20130731 |