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Delay-induced synchronization phenomena in an array of globally coupled logistic maps.

A C Martí1, C Masoller

  • 1Instituto de Física, Facultad de Ciencias, Universidad de la Republica, Iguá 4225, 11400 Montevideo, Uruguay.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
Summary

This study demonstrates how time-delayed coupling in logistic maps can achieve global synchronization. This coupling method suppresses chaos by stabilizing unstable periodic orbits, enabling predictable system behavior.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • Coupled map lattices are used to model complex spatio-temporal phenomena.
  • Synchronization in chaotic systems is a key area of research with applications in secure communication and neuroscience.
  • Time delays in interactions can significantly alter system dynamics and synchronization properties.

Purpose of the Study:

  • To investigate the synchronization dynamics of a linear array of globally coupled logistic maps with time-delayed coupling.
  • To analyze the effect of time-delayed mutual coupling on chaotic behavior in logistic maps.
  • To determine the conditions and parameter ranges for achieving global synchronization.

Main Methods:

  • Utilized a linear array of globally coupled identical logistic maps.

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  • Incorporated time-delayed coupling to account for finite interaction propagation velocity.
  • Performed stability analysis of the synchronized states.

    • Main Results:

    • Identified globally synchronized states where array elements follow a periodic orbit.
    • Observed that time-delayed coupling suppresses chaotic behavior in uncoupled maps.
    • Demonstrated stabilization of previously unstable periodic orbits by the delayed coupling.
    • Calculated the range of coupling strengths that yield global synchronization.

    Conclusions:

    • Time-delayed coupling is an effective mechanism for inducing global synchronization in coupled chaotic systems.
    • This synchronization is achieved by stabilizing unstable periodic orbits, leading to predictable dynamics.
    • The study provides a framework for understanding and controlling synchronization in complex systems with delayed interactions.