Local bifurcation analysis of a four-dimensional hyperchaotic system  

作　　者：吴文娟 陈增强 袁著祉 

机构地区：[1]Department of Automation,Nankai University

出　　处：《Chinese Physics B》2008年第7期2420-2432,共13页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos 60774088,10772135 and 60574036);the Research Foundation from the Ministry of Education of China (Grant Nos 107024 and 207005);the Program for New Century Excellent Talents in University of China (NCET);the Application Base and Frontier Technology Project of Tianjin,China(Grant No 08JCZDJC21900)

摘　　要：Local bifurcation phenomena in a four-dlmensional continuous hyperchaotic system, which has rich and complex dynamical behaviours, are analysed. The local bifurcations of the system are investigated by utilizing the bifurcation theory and the centre manifold theorem, and thus the conditions of the existence of pitchfork bifurcation and Hopf bifurcation are derived in detail. Numerical simulations are presented to verify the theoretical analysis, and they show some interesting dynamics, including stable periodic orbits emerging from the new fixed points generated by pitchfork bifurcation, coexistence of a stable limit cycle and a chaotic attractor, as well as chaos within quite a wide parameter region.Local bifurcation phenomena in a four-dlmensional continuous hyperchaotic system, which has rich and complex dynamical behaviours, are analysed. The local bifurcations of the system are investigated by utilizing the bifurcation theory and the centre manifold theorem, and thus the conditions of the existence of pitchfork bifurcation and Hopf bifurcation are derived in detail. Numerical simulations are presented to verify the theoretical analysis, and they show some interesting dynamics, including stable periodic orbits emerging from the new fixed points generated by pitchfork bifurcation, coexistence of a stable limit cycle and a chaotic attractor, as well as chaos within quite a wide parameter region.

关 键 词：HYPERCHAOS pitchfork bifurcation Hopf bifurcation centre manifold theorem 

分 类 号：O415.5[理学—理论物理] O231[理学—物理]