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Marzena Ciszak1, Catalina Mayol2, Claudio R Mirasso2

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This study explores anticipated synchronization in complex Ginzburg-Landau systems. The anticipation time depends on system dynamics and autocorrelation, with analytical stability conditions provided.

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Area of Science:

  • Nonlinear Dynamics
  • Complex Systems Theory
  • Chaos Theory

Background:

  • Complex Ginzburg-Landau equations model various phenomena.
  • Synchronization in coupled systems is a key research area.
  • Anticipated synchronization involves a master system predicting a slave system's behavior.

Purpose of the Study:

  • Investigate anticipated synchronization in master-slave complex Ginzburg-Landau systems.
  • Determine factors influencing anticipation time.
  • Establish analytical conditions for synchronization stability.

Main Methods:

  • Utilized master-slave configuration with complex-valued coupling.
  • Analyzed systems operating in different dynamical regimes (defect turbulence, phase turbulence, bichaos).
  • Derived analytical conditions for the stability of the synchronization manifold.

Main Results:

  • Anticipation time magnitude depends on the dynamical regime.
  • Largest anticipation time scales with the linear autocorrelation time.
  • Analytical stability conditions qualitatively agree with numerical findings.
  • Confirmed anticipated synchronization in 2D complex Ginzburg-Landau systems.

Conclusions:

  • Anticipated synchronization is achievable in coupled complex Ginzburg-Landau systems.
  • Dynamical regime and autocorrelation time are critical for anticipation.
  • Analytical methods can predict synchronization stability.