Torus Breakdown in Noninvertible Maps

V. Maistrenko, Yu. Maistrenko, Erik Mosekilde

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Abstract

We propose a criterion for the destruction of a two-dimensional torus through the formation of an infinite set of cusp points on the closed invariant curves defining the resonance torus. This mechanism is specific to noninvertible maps. The cusp points arise when the tangent to the torus at the point of intersection with the critical curve L-0 coincides with the eigendirection corresponding to vanishing eigenvalue for the noninvertible map. Further parameter changes lead typically to the generation of loops (self-intersections of the invariant manifolds) followed by the transformation of the torus into a complex chaotic set.
Original languageEnglish
JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume67
Issue number4
Pages (from-to)046215
ISSN1063-651X
DOIs
Publication statusPublished - 2003

Bibliographical note

Copyright (2003) American Physical Society

Keywords

  • CHAOS
  • QUASI-PERIODICITY
  • TRANSITION
  • LOCKING
  • SYSTEM
  • DESYNCHRONIZATION
  • BIFURCATIONS

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