CN103220126A - Unified multi-wing chaotic system - Google Patents

Unified multi-wing chaotic system Download PDF

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Publication number
CN103220126A
CN103220126A CN2013101403664A CN201310140366A CN103220126A CN 103220126 A CN103220126 A CN 103220126A CN 2013101403664 A CN2013101403664 A CN 2013101403664A CN 201310140366 A CN201310140366 A CN 201310140366A CN 103220126 A CN103220126 A CN 103220126A
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chaos
unified
wing
butterfly
multiple wing
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不公告发明人
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Abstract

The invention relates to a unified multi-wing chaotic system. A new method for generating multi-wing butterfly-shaped chaotic attractors is proposed. Based on a three-dimension unified chaotic system, and through the fact that a piecewise sign linear function is added, the unified multi-wing chaotic system is constructed. Through the fact that parameters and different sign functions are set, a unified multi-wing butterfly-shaped chaotic attractor can be obtained, and the feasibility and the effectiveness of the method for generating the multi-wing butterfly-shaped chaotic attractors are verified through experimental results. The unified multi-wing chaotic system can have wide application prospects and important application value in the fields of radars, secure communication, electronic countermeasures and the like.

Description

A kind of unified multiple wing chaos system
Technical field
The present invention relates to a kind of unified 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,
Figure 301707DEST_PATH_IMAGE001
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 proposes a kind of unified multiple wing chaos system on the basis of unified chaotic system, and has provided a kind of new method that produces the butterfly-shaped chaos attractor of multiple wing.Based on the three dimensional unification chaos system,, construct a kind of unified multiple wing chaos system by increasing a break sign linear function., by parameter is set
Figure 457882DEST_PATH_IMAGE002
And the distinct symbols function, can obtain the butterfly-shaped chaos attractor of unified multiple wing, 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 method of unifying the multiple wing chaos system and having provided the butterfly-like chaos attractor of its generation multiple wing.
In order to solve the problems of the technologies described above, to the invention provides that the present invention is a kind of to be improved on the unified chaotic system basis, and produce the new method of multiple wing butterfly chaos attractor.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 unification chaos system are:
(1)
Work as parameter The time, chaos is the Lorenz chaos system; When
Figure 709369DEST_PATH_IMAGE005
The time, chaos is
Figure 454471DEST_PATH_IMAGE001
Chaos system; When
Figure 891268DEST_PATH_IMAGE006
The time, chaos is the Chen chaos system, wherein
Figure 987400DEST_PATH_IMAGE007
,
Figure 682693DEST_PATH_IMAGE008
,
Figure 547881DEST_PATH_IMAGE009
Be state variable.
Equation (1) is carried out conversion, unified chaotic system
Figure 421159DEST_PATH_IMAGE010
, put in order then, can obtain partial differential is equation:
Figure 207849DEST_PATH_IMAGE011
(2)
Wherein, function
Figure 457565DEST_PATH_IMAGE012
For:
Figure 177259DEST_PATH_IMAGE013
(3)
Work as parameter
Figure 487018DEST_PATH_IMAGE014
When getting different numerical value respectively, can obtain the dissimilar butterfly-like chaos attractors of unified multiple wing.
Effect of the present invention and effect
(1) the present invention has realized providing a kind of unified multiple wing chaos system, works as parameter
Figure 977649DEST_PATH_IMAGE014
When getting different numerical value respectively, can obtain the dissimilar butterfly-like chaos attractors of unified multiple wing.
(2) adopt unified 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 it 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.
Fig. 1 for unified multiple wing chaos system produce the butterfly-like chaos attractor two dimension of 4 wing chaos phasor (
Figure 686847DEST_PATH_IMAGE004
).
Fig. 2 for unified multiple wing chaos system produce the butterfly-like chaos attractor two dimension of 4 wing chaos phasor (
Figure 526627DEST_PATH_IMAGE005
).
Fig. 3 for unified multiple wing chaos system produce the butterfly-like chaos attractor two dimension of 4 wing chaos phasor (
Figure 476129DEST_PATH_IMAGE006
).
Fig. 4 for unified multiple wing chaos system produce the butterfly-like chaos attractor two dimension of 6 wing chaos phasor ( ).
Embodiment
The pairing partial differential equation of described three dimensional unification chaos system are:
(1)
Work as parameter
Figure 54375DEST_PATH_IMAGE004
The time, chaos is the Lorenz chaos system; When
Figure 174778DEST_PATH_IMAGE005
The time, chaos is
Figure 174089DEST_PATH_IMAGE001
Chaos system; When The time, chaos is the Chen chaos system, wherein
Figure 118091DEST_PATH_IMAGE007
,
Figure 409395DEST_PATH_IMAGE008
,
Figure 410849DEST_PATH_IMAGE009
Be state variable.
Equation (1) is carried out conversion, unified chaotic system , put in order then, can obtain partial differential is equation:
Figure 481890DEST_PATH_IMAGE011
(2)
Wherein, function For:
Figure 213272DEST_PATH_IMAGE013
(3)
Work as parameter
Figure 950284DEST_PATH_IMAGE014
When getting different numerical value respectively, can obtain the dissimilar butterfly-like chaos attractors of unified multiple wing.Work as parameter
Figure 208090DEST_PATH_IMAGE015
The time, the butterfly-like chaos attractor of its 4 wing is as shown in Figure 1; Work as parameter
Figure 841196DEST_PATH_IMAGE016
The time, the butterfly-like chaos attractor of its 4 wing is as shown in Figure 2; Work as parameter
Figure 82822DEST_PATH_IMAGE017
The time, the butterfly-like chaos attractor of its 4 wing is as shown in Figure 3; Work as parameter
Figure 357945DEST_PATH_IMAGE018
The time, the butterfly-like chaos attractor of its 6 wing is as shown in Figure 4; From Fig. 1, Fig. 2, Fig. 3 and Fig. 4 as can be seen, above-mentioned unified multiple wing chaos system is in parameter
Figure 470258DEST_PATH_IMAGE014
When getting different numerical value respectively, can obtain the dissimilar butterfly-like chaos attractors of unified multiple wing.
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. unified multiple wing chaos system, its feature comprises: the present invention proposes and a kind ofly improve on the unified chaotic system basis, and the new method of generation multiple wing butterfly chaos attractor. the quantic of the chaos system of this method construct is simple, this system has bigger using value on engineering, especially the application in secure communication.
2. three dimensional unification multiple wing chaos system according to claim 1 is characterized in that, the pairing partial differential equation of described three dimensional unification chaos system are:
Figure 258520DEST_PATH_IMAGE001
(1)
Wherein, work as parameter
Figure 217249DEST_PATH_IMAGE002
The time, chaos is the Lorenz chaos system; When
Figure 544325DEST_PATH_IMAGE003
The time, chaos is
Figure 297517DEST_PATH_IMAGE004
Chaos system; When
Figure 178886DEST_PATH_IMAGE005
The time, chaos is the Chen chaos system, wherein
Figure 941305DEST_PATH_IMAGE006
,
Figure 351251DEST_PATH_IMAGE007
, Be state variable.
3. three dimensional unification multiple wing chaos system according to claim 1 is characterized in that: equation (1) is carried out conversion, unified chaotic system
Figure 909588DEST_PATH_IMAGE009
, put in order then, can obtain partial differential is equation:
(2)
Wherein, function For:
Figure 341204DEST_PATH_IMAGE012
(3)
Work as parameter
Figure 446432DEST_PATH_IMAGE013
When getting different numerical value respectively, can obtain the dissimilar butterfly-like chaos attractors of unified multiple wing.
CN2013101403664A 2013-04-23 2013-04-23 Unified multi-wing chaotic system Pending CN103220126A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103957098A (en) * 2014-04-14 2014-07-30 重庆邮电大学 Chaotic circuit for producing multiple butterfly-shaped attractors and implementation method

Citations (3)

* Cited by examiner, † Cited by third party
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

Patent Citations (3)

* Cited by examiner, † Cited by third party
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 (1)

* Cited by examiner, † Cited by third party
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技术辑》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103957098A (en) * 2014-04-14 2014-07-30 重庆邮电大学 Chaotic circuit for producing multiple butterfly-shaped attractors and implementation method
CN103957098B (en) * 2014-04-14 2017-05-10 重庆邮电大学 Chaotic circuit for producing multiple butterfly-shaped attractors and implementation method

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Application publication date: 20130724