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Sequence of Routes to Chaos in a Lorenz-Type System

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  • Fangyan Yang
  • Yongming Cao
  • Lijuan Chen
  • Qingdu Li

Abstract

This paper reports a new bifurcation pattern observed in a Lorenz-type system. The pattern is composed of a main bifurcation route to chaos ( ) and a sequence of sub-bifurcation routes with isolated sub-branches to chaos. When is odd, the isolated sub-branches are from a period- limit cycle, followed by twin period- limit cycles via a pitchfork bifurcation, twin chaotic attractors via period-doubling bifurcations, and a symmetric chaotic attractor via boundary crisis. When is even, the isolated sub-branches are from twin period- limit cycles, which become twin chaotic attractors via period-doubling bifurcations. The paper also shows that the main route and the sub-routes can coexist peacefully by studying basins of attraction.

Suggested Citation

  • Fangyan Yang & Yongming Cao & Lijuan Chen & Qingdu Li, 2020. "Sequence of Routes to Chaos in a Lorenz-Type System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-10, January.
    • Handle: RePEc:hin:jnddns:3162170
    DOI: 10.1155/2020/3162170
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    Cited by:

    1. Rao, XiaoBo & Gao, JianShe & Ding, ShunLiang & Liang, Jie & Zhang, Jiangang, 2023. "Multistability of gaits, the basin of attraction and its external topology in the simplest passive walking model on stairs," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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