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Synchronization in driven versus autonomous coupled chaotic maps.

M Pineda1, M G Cosenza

  • 1Max-Planck-Institut für Physik Komplexer Systeme, Nöthnizer Strasse 38, 01187 Dresden, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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This study compares synchronization in driven and autonomous coupled map systems. While both achieve chaotic synchronization, the driven system also synchronizes unstable periodic orbits, offering distinct collective states.

Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • Coupled map lattices (CMLs) are used to model complex systems with spatially extended dynamics.
  • Synchronization is a key phenomenon in nonlinear systems, observed in both natural and artificial systems.
  • External driving and global interactions are common perturbations influencing synchronization in CMLs.

Purpose of the Study:

  • To compare synchronization phenomena in a driven CML with local coupling versus an autonomous CML with local and global coupling.
  • To investigate the equivalence and differences in chaotic synchronized states and subsequent collective behaviors.
  • To determine the specific synchronization capabilities induced by external driving versus global interaction.

Main Methods:

  • Numerical simulations of locally coupled map lattices under external driving.

Related Experiment Videos

  • Analysis of an autonomous coupled map system incorporating both local and global interactions.
  • Comparison of emergent collective states and synchronization properties in both system types.

    • Main Results:

    • Chaotic synchronized states in both driven and autonomous systems are found to be equivalent.
    • Collective states emerging after instability of chaotic synchronization can differ between the two systems.
    • External driving induces synchronization of unstable periodic orbits in the driven lattice.
    • Global interaction in the autonomous system enables chaotic synchronization not achievable with local coupling alone.

    Conclusions:

    • Both external driving and global interaction can induce chaotic synchronization in coupled map systems.
    • The specific mechanisms (driving vs. global coupling) lead to distinct post-synchronization collective behaviors.
    • The study highlights the nuanced ways external perturbations shape synchronization in complex dynamical systems.