Periodic occurrence of chaotic behavior of homoclinic tangles

Q. D. Wang, A. Oksasoglu

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

In this article, we illustrate, through numerical simulations, some important aspects of the dynamics of the periodically perturbed homoclinic solutions for a dissipative saddle. More explicitly, we demonstrate that, when homoclinic tangles are created, three different dynamical phenomena, namely, horseshoes, periodic sinks, and attractors with Sinai-Ruelle-Bowen measures, manifest themselves periodically with respect to the magnitude of the forcing function. In addition, when the stable and the unstable manifolds are pulled apart so as not to intersect, first, rank 1 attractors, then quasi-periodic attractors are added to the dynamical scene.

Original languageEnglish (US)
Pages (from-to)387-395
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume239
Issue number7
DOIs
StatePublished - Apr 1 2010

Keywords

  • Chaos
  • Dissipative saddle

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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