Local bifurcation analysis of a four-dimensional hyperchaotic system

• 来源期刊: 中国物理B（英文版）
• 关键词: hyperchaos pitchfork bifurcation Hopf bifurcation centre manifold theorem
• 年，卷（期）: 2008,（7）
• 页码范围: 2420-2432
• 页数: 13页
• 语种: 英文

摘要

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.