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  • 标题:Sequence of Routes to Chaos in a Lorenz-Type System
  • 本地全文:下载
  • 作者:Fangyan Yang ; Yongming Cao ; Lijuan Chen
  • 期刊名称:Discrete Dynamics in Nature and Society
  • 印刷版ISSN:1026-0226
  • 电子版ISSN:1607-887X
  • 出版年度:2020
  • 卷号:2020
  • 页码:1-10
  • DOI:10.1155/2020/3162170
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    This paper reports a new bifurcation pattern observed in a Lorenz-type system. The pattern is composed of a main bifurcation route to chaos ( n = 1 ) and a sequence of sub-bifurcation routes with n = 3 , 4 , 5 , … , 14 isolated sub-branches to chaos. When n is odd, the n isolated sub-branches are from a period- n limit cycle, followed by twin period- n limit cycles via a pitchfork bifurcation, twin chaotic attractors via period-doubling bifurcations, and a symmetric chaotic attractor via boundary crisis. When n is even, the n isolated sub-branches are from twin period- n / 2 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.

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