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

Christian Reick and Erik Mosekilde
Phys. Rev. E 52, 1418 – Published 1 August 1995
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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.

  • Received 13 December 1994

DOI:https://doi.org/10.1103/PhysRevE.52.1418

©1995 American Physical Society

Authors & Affiliations

Christian Reick

  • I. Institut für Theoretische Physik, Universität Hamburg, D-20355 Hamburg, Germany

Erik Mosekilde

  • Physics Department, Center for Chaos and Turbulence Studies, The Technical University of Denmark, DK-2800 Lyngby, Denmark

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Vol. 52, Iss. 2 — August 1995

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