Transitions from phase-locked dynamics to chaos in a piecewise-linear map

Z.T. Zhusubaliyev, Erik Mosekilde, S. De, S. Banerjee

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Abstract

Recent work has shown that torus formation in piecewise-smooth maps can take place through a special type of border-collision bifurcation in which a pair of complex conjugate multipliers for a stable cycle abruptly jump out of the unit circle. Transitions from an ergodic to a resonant torus take place via border-collision fold bifurcations. We examine the transition to chaos through torus destruction in such maps. Considering a piecewise-linear normal-form map we show that this transition, by virtue of the interplay of border-collision bifurcations with period-doubling and homoclinic bifurcations, can involve mechanisms that differ qualitatively from those described by Afraimovich and Shilnikov.
Original languageEnglish
JournalPhysical Review E
Volume77
Issue number2
Pages (from-to)026206
ISSN2470-0045
DOIs
Publication statusPublished - 2008

Bibliographical note

Copyright 2008 American Physical Society

Keywords

  • SYSTEMS
  • TORUS
  • BORDER-COLLISION BIFURCATIONS
  • SMOOTH MAPS
  • GRAZING BIFURCATIONS
  • SWITCHING-CIRCUITS
  • CONVERTER
  • BIRTH

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