| GENERAL |
|
|
|
|
Analysis of Chaotic Dynamics in a Two-Dimensional Sine Square Map |
| XU Jie1, LONG Ke-Ping1, FOURNIER-PRUNARET Dani`ele2, TAHA Abdel-Kaddous2, CHARGE Pascal2 |
| 1School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu 6117312LATTIS, INSA, Toulouse University, 135 avenue de Rangueil 31077 Toulouse 4, France |
|
| Cite this article: |
|
XU Jie, LONG Ke-Ping, FOURNIER-PRUNARET Dani`ele et al 2010 Chin. Phys. Lett. 27 020504 |
|
|
|
|
Abstract We study an N-dimensional system based upon a sine map, which is related to the simplified model of an opto-electronic system. The system behavior is analyzed with the tools of nonlinear dynamics (bifurcations in the parameter plane, critical manifolds, basins of attraction, chaotic attractors). Our study relies on a two-dimensional system (N=2). It is interesting that this system shows the existence of bounded chaotic orbits, which can be considered for secure transmissions.
|
| Keywords:
05.45.Ac
05.45.Gg
05.45.Pq
|
|
|
Received: 06 November 2009
Published: 08 February 2010
|
|
| PACS: |
05.45.Ac
|
(Low-dimensional chaos)
|
| |
05.45.Gg
|
(Control of chaos, applications of chaos)
|
| |
05.45.Pq
|
(Numerical simulations of chaotic systems)
|
|
|
|
|
|
[1] Larger L and Fournier-Prunaret D 2005 European Conference on Circuit Theory and Design (Cork, Ireland 28 August--2 September 2005) I$\!$I p 161
[2] Larger L, Genin E, Udaltsov V S and Poinsot S 2005 J. Opt. Technol. 72 29
[3] Bischi G I, Mamman C and Gardini L 2000 Chaos, Solitons \& Fractals 11 543
[4] Xu J 2006 Congr\`es des Doctorants EDSYS (Tarbes, France 11 May 2006) p 35
[5] Charg\'e P, Xu J, Fournier-Prunaret D and Taha A K 2007 15th IEEE International Workshop on Nonlinear Dynamics of Electronic Systems (Tokushima, Japan 23--26 July 2007) p 141
[6] Mira C 1987 Chaotic Dynamics (Singapore: World Scientific) chap 1 p 59
[7] Carcass\`es J P 1993 Int. J. Bif. Chaos 3 869
[8] Mira C, Gardini L, Barugola A and Cathala J C 1996 World Scientific Series A 20 636
[9] Canovas J 2001 Chaos, Solitons \& Fractals 12 1259
[10] Mira C, Fournier-Prunaret D, Gardini L, Kawakami H and Cathala J C 1994 Int. J. Bifur. Chaos Appl. Sci. Engin. 4 343
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
