Local bifurcation analysis of a four-dimensional hyperchaotic system |
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Authors: | Wu Wen-Juan Chen Zeng-Qiang and Yuan Zhu-Zhi |
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Institution: | Department of Automation, Nankai University, Tianjin
300071,
China |
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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. |
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Keywords: | hyperchaos pitchfork
bifurcation Hopf bifurcation centre manifold theorem |
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