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

Zhanybai T. Zhusubaliyev, Erik Mosekilde, Soma De, and Soumitro Banerjee
Phys. Rev. E 77, 026206 – Published 11 February 2008

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.

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  • Received 27 October 2007

DOI:https://doi.org/10.1103/PhysRevE.77.026206

©2008 American Physical Society

Authors & Affiliations

Zhanybai T. Zhusubaliyev*

  • Kursk State Technical University, Dept. of Computer Science, 50 Years of October Street, 94, Kursk 305040, Russia

Erik Mosekilde

  • Complex Systems Group, Department of Physics, The Technical University of Denmark, 2800 Lyngby, Denmark

Soma De

  • Department of Mathematics and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur-721302, India

Soumitro Banerjee§

  • Department of Electrical Engineering and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur-721302, India

  • *zhanybai@mail.kursk.ru
  • Erik.Mosekilde@fysik.dtu.dk
  • soma@cts.iitkgp.ernet.in
  • §soumitro@ee.iitkgp.ernet.in

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Issue

Vol. 77, Iss. 2 — February 2008

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