Scaling properties of bicritical dynamics in unidirectionally coupled period-doubling systems in the presence of noise

J.V. Kapustina, A.P. Kuznetsov, S.P. Kuznetsov, Erik Mosekilde

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Abstract

We study scaling regularities associated with the effects of additive noise on the bicritical behavior of a system of two unidirectionally coupled quadratic maps. A renormalization group analysis of the effects of noise is developed. We outline the qualitative and quantitative differences between the response of the system to random perturbations added to the master subsystem or the slave subsystem. The universal constants determining the rescaling rules for the intensity of the noise sources in the master and slave subsystems are found to be gamma = 6.619036... and v = 2.713708....respectively. A number of computer graphical illustrations for the scaling regularities is presented. We discuss the smearing of the fine structure of the bicritical attractor and the Fourier spectra in the presence of noise, the self-similar structure of the Lyapunov charts on the parameter plane near the bicritical point, and the shift of the threshold of hyperchaos in dependence of the noise intensity.
Original languageEnglish
JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume64
Issue number6
Pages (from-to)066207
ISSN1063-651X
DOIs
Publication statusPublished - 2001

Bibliographical note

Copyright (2001) American Physical Society

Keywords

  • CHAOS
  • ONSET
  • QUASI-PERIODICITY
  • INTERMITTENCY
  • TRANSITION
  • CIRCLE
  • MAPS
  • BEHAVIOR
  • RENORMALIZATION-GROUP ANALYSIS
  • DISSIPATIVE SYSTEMS

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