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Related Experiment Videos

First-order synchronization transition in locally coupled maps.

P K Mohanty1

  • 1Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel 76100.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
PubMed
Summary

Coupling chaotic maps on lattices shows a phase transition to synchronization. Unexpectedly, the largest Lyapunov exponent turns positive at this point, indicating a shift in system dynamics.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Statistical physics

Background:

  • Diffusively coupled chaotic maps on lattices exhibit complex behaviors.
  • Alternating sublattice updates introduce effective time delays.
  • Understanding phase transitions in coupled chaotic systems is crucial.

Purpose of the Study:

  • Investigate phase transitions in diffusively coupled chaotic maps on d-dimensional square lattices.
  • Analyze the role of coupling strength and map differentiability on system dynamics.
  • Clarify the behavior of the largest Lyapunov exponent at the synchronization transition.

Main Methods:

  • Simulations of diffusively coupled chaotic maps on periodic d-dimensional square lattices.
  • Alternating updates of even and odd sublattices to introduce delay.

Related Experiment Videos

  • Calculation of the largest Lyapunov exponent to characterize system stability and chaos.

    • Main Results:

    • A first-order phase transition from a multistable to a synchronized phase was observed as coupling strength increased.
    • The largest Lyapunov exponent changed sign at the transition point, contrary to previous predictions.
    • Further increases in coupling strength led to desynchronization, with the phase space splitting into two ergodic regions.

    Conclusions:

    • The synchronization transition in this system is characterized by a sign change in the largest Lyapunov exponent.
    • The nature of the desynchronization transition is dependent on the differentiability of the chaotic maps.
    • This study provides new insights into the dynamics of coupled chaotic systems and their phase transitions.