A computer-assisted study of global dynamic transitions for a noninvertible system

Raymond A. Adomaitis, Ioannis G. Kevrekidis, Rafael De La Llave

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We present a computer-assisted analysis of the phase space features and bifurcations of a non-invertible, discrete-time system. Our focus is on the role played by noninvertibility in generating disconnected basins of attraction and the breakup of invariant circle solutions. Transitions between basin of attraction structures are identified and organized according to "levels of complexity," a term we define in this paper. In particular, we present an algorithm that provides a computational approximation to the boundary (in phase space) separating points with different preimage behavior. The interplay between this boundary and other phase space features is shown to be crucial in understanding global bifurcations and transitions in the structure of the basin of attraction.

Original languageEnglish (US)
Pages (from-to)1305-1321
Number of pages17
JournalInternational Journal of Bifurcation and Chaos
Volume17
Issue number4
DOIs
StatePublished - Apr 2007

All Science Journal Classification (ASJC) codes

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

Keywords

  • Basin of attraction
  • Invariant circles
  • Logistic map
  • Noninvertibility

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