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Multichannel intermittencies induced by symmetries.

Christophe Letellier1, Pierre Werny, Jean-Marc Malasoma

  • 1CORIA UMR 6614, Université de Rouen, Avenue de l'Université, Boîte Postale 12, F-76801 Saint-Etienne du Rouvray Cedex, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 9, 2002
PubMed
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Type-I intermittencies, common in dynamical systems, can exhibit multiple reinjection channels. This study demonstrates that n-channel intermittencies arise from n coexisting stable periodic orbits linked by symmetry.

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Nonlinear Dynamics
  • Mathematical Physics

Background:

  • Type-I intermittencies are frequently observed in nonlinear systems near periodic windows.
  • Typically, these intermittencies feature a single reinjection channel, meaning only one type of laminar phase is observed.
  • Recent studies have identified instances of type-I intermittencies with multiple reinjection channels.

Purpose of the Study:

  • To investigate the underlying mechanism of type-I intermittencies with multiple reinjection channels.
  • To establish a theoretical framework connecting n-channel intermittencies to the coexistence of stable periodic orbits.
  • To develop a general procedure for constructing systems exhibiting type-I intermittencies with n reinjection channels.

Main Methods:

Related Experiment Videos

  • Theoretical analysis of dynamical systems exhibiting type-I intermittency.
  • Utilizing the concept of the n-fold cover of an image system to construct multi-channel intermittencies.
  • Explicit construction and analysis of cases for n=2 and n=3 using the centered Rössler system.

    • Main Results:

    • Type-I intermittencies with n reinjection channels are mathematically associated with the coexistence of n stable periodic orbits.
    • These stable periodic orbits are shown to be mapped into each other under a system symmetry.
    • A systematic procedure is presented for generating type-I intermittencies with n channels.

    Conclusions:

    • The coexistence of n symmetry-related stable periodic orbits is the key to n-channel type-I intermittencies.
    • The n-fold cover construction provides a method to realize and study these complex intermittency behaviors.
    • This work extends the understanding of intermittency phenomena in nonlinear dynamical systems.