Chaotic attractors in one-dimension generated by a singular Shilnikov orbit

Krista J. Taylor, Bo Deng

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Chaotic attractors containing Shilnikov's saddle-focus homoclinic orbits have been observed in many physical systems. Past and current researches of this type of Shilnikov homoclinic phenomena have focused on the orbit and nearby structures only. In this paper we will look at the role such orbits play in a type of attractor, which arises from one-dimensional return maps at the singular limits of some singularly perturbed systems. Results on symbolic dynamics, natural measures, and Lyapunov exponents are obtained for a sequence of a one-parameter caricature family of such attractors.

Original languageEnglish (US)
Pages (from-to)3059-3083
Number of pages25
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume11
Issue number12
DOIs
StatePublished - Jan 1 2001

Fingerprint

Chaotic Attractor
One Dimension
Attractor
Orbits
Orbit
Return Map
Singularly Perturbed Systems
Singular Limit
One-dimensional Maps
Symbolic Dynamics
Homoclinic
Homoclinic Orbit
Saddle
Lyapunov Exponent
Family

ASJC Scopus subject areas

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

Cite this

Chaotic attractors in one-dimension generated by a singular Shilnikov orbit. / Taylor, Krista J.; Deng, Bo.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 11, No. 12, 01.01.2001, p. 3059-3083.

Research output: Contribution to journalArticle

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