Transverse instability and riddled basins in a system of two coupled logistic maps

Yu.L. Maistrenko, V.L. Maistrenko, A. Popovich, Erik Mosekilde

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Abstract

The paper examines the conditions for the appearance of riddled basins of attraction for a system of two symmetrically coupled logistic maps. We determine the regions in parameter space where the transverse Lyapunov exponent is negative and obtain the bifurcation curves for the transverse destabilization of low-periodic orbits embedded in the synchronized chaotic state. The changes in the attractor and its basin of attraction when scanning accross the riddling and blowout bifurcations are explained.
Original languageEnglish
JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume57
Issue number3
Pages (from-to)2713-2724
ISSN1063-651X
DOIs
Publication statusPublished - 1998

Bibliographical note

Copyright (1998) by the American Physical Society.

Keywords

  • SADDLE
  • STABILITY THEORY
  • CHAOTIC ATTRACTORS
  • INTERMITTENCY
  • DYNAMICAL-SYSTEMS
  • SYNCHRONIZED MOTION
  • BIFURCATION
  • PERIODIC-ORBITS
  • OSCILLATOR SYSTEMS

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