Quasiattractors and homoclinic tangencies

S. V. Gonchenko, L. P. Shil'nikov, D. V. Turaev

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

Recent results describing nontrivial dynamical phenomena in systems with homoclinic tangencies are represented. Such systems cover a large variety of dynamical models known from natural applications and it is established that so-called quasiattractors of these systems may exhibit rather nontrivial features which are in a sharp distinction, with that one could expect in analogy with hyperbolic or Lorenz-like attractors. For instance, the impossibility of giving a finite-parameter complete description of dynamics and bifurcations of the quasiattractors is shown. Besides, it is shown that the quasiattractors may simultaneously contain saddle periodic orbits with different numbers of positive Lyapunov exponents. If the dimension of a phase space is not too low (greater than four for flows and greater than three for maps), it is shown that such a quasiattractor may contain infinitely many coexisting strange attractors.

Original languageEnglish
Pages (from-to)195-227
Number of pages33
JournalComputers and Mathematics with Applications
Volume34
Issue number2-4
DOIs
StatePublished - 1 Jan 1997
Externally publishedYes

Keywords

  • Attractor
  • Dynamical models
  • Homoclinic bifurcations

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