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Dynamics of a New Hyperchaotic System with Only One Equilibrium Point

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  • Xiang Li
  • Ranchao Wu

Abstract

A new 4D hyperchaotic system is constructed based on the Lorenz system. The compound structure and forming mechanism of the new hyperchaotic attractor are studied via a controlled system with constant controllers. Furthermore, it is found that the Hopf bifurcation occurs in this hyperchaotic system when the bifurcation parameter exceeds a critical value. The direction of the Hopf bifurcation as well as the stability of bifurcating periodic solutions is presented in detail by virtue of the normal form theory. Numerical simulations are given to illustrate and verify the results.

Suggested Citation

  • Xiang Li & Ranchao Wu, 2013. "Dynamics of a New Hyperchaotic System with Only One Equilibrium Point," Journal of Mathematics, Hindawi, vol. 2013, pages 1-9, July.
    • Handle: RePEc:hin:jjmath:935384
    DOI: 10.1155/2013/935384
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    References listed on IDEAS

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    1. Zhou, Xiaobing & Wu, Yue & Li, Yi & Wei, Zhengxi, 2008. "Hopf bifurcation analysis of the Liu system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1385-1391.
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