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Si’lnikov chaos and Hopf bifurcation analysis of Rucklidge system

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  • Wang, Xia

Abstract

A three-dimensional autonomous system – the Rucklidge system is considered. By the analytical method, Hopf bifurcation of Rucklidge system may occur when choosing an appropriate bifurcation parameter. Using the undetermined coefficient method, the existence of heteroclinic and homoclinic orbits in the Rucklidge system is proved, and the explicit and uniformly convergent algebraic expressions of Si’lnikov type orbits are given. As a result, the Si’lnikov criterion guarantees that there exists the Smale horseshoe chaos motion for the Rucklidge system.

Suggested Citation

  • Wang, Xia, 2009. "Si’lnikov chaos and Hopf bifurcation analysis of Rucklidge system," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2208-2217.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2208-2217
    DOI: 10.1016/j.chaos.2009.03.137
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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.
    2. Čelikovský, Sergej & Chen, Guanrong, 2005. "On the generalized Lorenz canonical form," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1271-1276.
    3. Vicha, T. & Dohnal, M., 2008. "Qualitative feature extractions of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 364-373.
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    Cited by:

    1. Vignesh, D. & He, Shaobo & Banerjee, Santo, 2023. "Modelling discrete time fractional Rucklidge system with complex state variables and its synchronization," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    2. Maria Santos Bruzón & Gaetana Gambino & Maria Luz Gandarias, 2021. "Generalized Camassa–Holm Equations: Symmetry, Conservation Laws and Regular Pulse and Front Solutions," Mathematics, MDPI, vol. 9(9), pages 1-20, April.

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