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Synchronizing noisy nonidentical oscillators by transient uncoupling.

Aditya Tandon1, Malte Schröder2, Manu Mannattil1

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Transient uncoupling enables generalized synchronization in nonidentical chaotic systems, even when standard coupling fails. This method also enhances synchronization stability against common noise by selectively pausing coupling during phase space divergence.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • Synchronization involves coupled identical units achieving identical dynamics.
  • Generalized synchronization describes a functional relationship between nonidentical units after transients.
  • Transient uncoupling is a recent technique for synchronizing identical units.

Purpose of the Study:

  • To investigate the applicability of transient uncoupling to generalized synchronization in nonidentical chaotic systems.
  • To determine if transient uncoupling can achieve generalized synchronization where regular coupling fails.
  • To assess the impact of transient uncoupling on synchronization stability in the presence of common noise.

Main Methods:

  • Applying the concept of transient uncoupling to nonidentical chaotic units.
  • Comparing generalized synchronization achieved by transient uncoupling versus regular coupling.
  • Analyzing the stabilizing effect of transient uncoupling on synchronization under common noise.
  • Developing a method to identify optimal uncoupling regions based on local phase space divergence by linearizing the flow.

Main Results:

  • Transient uncoupling successfully induces generalized synchronization among nonidentical chaotic units.
  • Generalized synchronization was achieved via transient uncoupling in scenarios where regular coupling was ineffective.
  • Transient uncoupling demonstrated a stabilizing effect on synchronization when subjected to common noise.
  • A method for selecting favorable uncoupling regions based on local divergence measurement was proposed and validated.

Conclusions:

  • Transient uncoupling is a viable and effective strategy for achieving generalized synchronization in nonidentical chaotic systems.
  • This technique offers advantages over traditional coupling methods, particularly in challenging scenarios and noisy environments.
  • The proposed method for identifying uncoupling regions enhances the robustness and applicability of transient uncoupling.