Chaotic Dynamics in a Sine Square Map: High-Dimensional Case (N≥3)
XU Jie1, LONG Ke-Ping1, FOURNIER-PRUNARET Danièle2, TAHA Abdel-Kaddous2, CHARGE Pascal2
1School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu 611731 2LATTIS, INSA, Toulouse University, 135 avenue de Rangueil 31077 Toulouse 4, France
Chaotic Dynamics in a Sine Square Map: High-Dimensional Case (N≥3)
XU Jie1, LONG Ke-Ping1, FOURNIER-PRUNARET Danièle2, TAHA Abdel-Kaddous2, CHARGE Pascal2
1School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu 611731 2LATTIS, INSA, Toulouse University, 135 avenue de Rangueil 31077 Toulouse 4, France
We study an N-dimensional system based on a sine square map and analyze the system behaviors of cases of dimension N≥3 with the tools of nonlinear dynamics. In the three-dimensional case, bifurcations in the parameter plane, invariant manifolds, critical manifolds and chaotic attractors are studied. Then we extend this study to the cases of higher dimension (N>3) to understand generalized properties of the system. The analysis and experimental results of the system demonstrate the existence of bounded chaotic orbits, which can be considered for secure transmissions.
We study an N-dimensional system based on a sine square map and analyze the system behaviors of cases of dimension N≥3 with the tools of nonlinear dynamics. In the three-dimensional case, bifurcations in the parameter plane, invariant manifolds, critical manifolds and chaotic attractors are studied. Then we extend this study to the cases of higher dimension (N>3) to understand generalized properties of the system. The analysis and experimental results of the system demonstrate the existence of bounded chaotic orbits, which can be considered for secure transmissions.
XU Jie;LONG Ke-Ping;FOURNIER-PRUNARET Danièle;TAHA Abdel-Kaddous;CHARGE Pascal. Chaotic Dynamics in a Sine Square Map: High-Dimensional Case (N≥3)[J]. 中国物理快报, 2010, 27(8): 80506-080506.
XU Jie, LONG Ke-Ping, FOURNIER-PRUNARET Danièle, TAHA Abdel-Kaddous, CHARGE Pascal. Chaotic Dynamics in a Sine Square Map: High-Dimensional Case (N≥3). Chin. Phys. Lett., 2010, 27(8): 80506-080506.
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2010, Vol. 27 
