Abstract Local bifurcation phenomena in a four-dimensional 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.
Received: 20 December 2007
Revised: 10 January 2008
Accepted manuscript online:
Fund: Project 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), and the Application Base and Frontier
Technology Project of Tianjin, China (Grant No 08JCZDJC21900).
Cite this article:
Wu Wen-Juan(吴文娟), Chen Zeng-Qiang(陈增强), and Yuan Zhu-Zhi(袁著祉) Local bifurcation analysis of a four-dimensional hyperchaotic system 2008 Chin. Phys. B 17 2420
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