Showcase of blue sky catastrophes

Leonid Pavlovich Shilnikov, Andrey L. Shilnikov, Dmitry V. Turaev

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

Let a system of differential equations possess a saddle periodic orbit such that every orbit in its unstable manifold is homoclinic, i.e. the unstable manifold is a subset of the (global) stable manifold. We study several bifurcation cases of the breakdown of such a homoclinic connection that causes the blue sky catastrophe, as well as the onset of complex dynamics. The birth of an invariant torus and a Klein bottle is also described.

Original languageEnglish
Article number1440003
JournalInternational Journal of Bifurcation and Chaos
Volume24
Issue number8
DOIs
StatePublished - 1 Jan 2014
Externally publishedYes

Keywords

  • Codimension-one
  • blue sky catastrophe
  • homoclinic bifurcations

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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