Antimonotonicity: inevitable reversals of period-doubling cascades

Silvina P. Dawson, Celso Grebogi, James A. Yorke, Ittai Kan, Huseyin Kocak

Research output: Contribution to journalArticle

109 Citations (Scopus)

Abstract

In many common nonlinear dynamical systems depending on a parameter, it is shown that periodic orbit creating cascades must be accompanied by periodic orbit annihilating cascades as the parameter is varied. Moreover, reversals from a periodic orbit creating cascade to a periodic orbit annihilating one must occur infinitely often in the vicinity of certain common parameter values. It is also demonstrated that these inevitable reversals are indeed observable in specific chaotic systems.

Original languageEnglish
Pages (from-to)249-254
Number of pages6
JournalPhysics Letters A
Volume162
Issue number3
DOIs
Publication statusPublished - 10 Feb 1992

Keywords

  • chaotic behavior
  • bifurcation
  • oscillator
  • transition
  • creation
  • sequence
  • system
  • laser
  • maps

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