Emergence of quasiperiodicity in symmetrically coupled, identical period-doubling systems

Christian Reick, Erik Mosekilde

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Abstract

When two Identical period-doubling systems are coupled symmetrically, the period-doubling transition to chaos may be replaced by a quasiperiodic transition. The reason for this is that at an early stage of the period-doubling cascade, a Hopf bifurcation instead of a period-doubling bifurcation occurs. Our main result is that the emergence of this Hopf bifurcation is a generic phenomenon in symmetrically coupled, identical period-doubling systems. The whole phenomenon is stable against small nonsymmetric perturbations. Our results cover maps and differential equations of arbitrary dimension. As a consequence the Feigenbaum transition to chaos in these coupled systems-which exists, but tends to be unstable-is accompanied by an infinity of Hopf bifurcations.
Original languageEnglish
JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume52
Issue number2
Pages (from-to)1418-1435
ISSN1063-651X
DOIs
Publication statusPublished - 1995

Bibliographical note

Copyright (1995) by the American Physical Society.

Keywords

  • MODEL
  • TRANSITION
  • SIMULATIONS
  • CHEMICAL OSCILLATORS
  • MAPS
  • BIFURCATIONS
  • CHAOTIC BEHAVIOR
  • DYNAMICS

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