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 parame...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.展开更多
基金Supported by Chang Jiang Scholars Program of the Ministry of Education of China, the National Natural Science Foundation of China for Distinguished Young Scholars under Grant No 60725104, the National Basic Research Program of China under Grant No 2007CB310706, the National High-Technology Research and Development Program of China under Grant Nos 2008AA011001, 2008AA011002, 2009AA01Z254 and 2009AA01Z215, the National Natural Science Foundation of China under Grant Nos 60873263, 60932002 and 60932005, Youth Foundation of UESTC under Grant No L0801010jx0815, NCET Program of MoE of China, and the French Project ANR05R.NRT02001 ACSCOM.
文摘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.
