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Taming chimeras in coupled oscillators using soft actor-critic based reinforcement learning.

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We developed a model-free deep reinforcement learning method to control chimera states in coupled oscillators. This approach precisely positions coherent and incoherent domains, offering versatile control over complex dynamical systems.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Chimera states, a unique pattern of coexisting coherent and incoherent domains in coupled oscillator systems, present a fascinating challenge in nonlinear dynamics.
  • Existing control methods often require detailed system knowledge, limiting their applicability.
  • Understanding and controlling chimera states is crucial for applications ranging from neuroscience to power grids.

Purpose of the Study:

  • To propose a universal, model-free method for controlling chimera states in coupled oscillators.
  • To precisely manipulate the spatial positions of coherent and incoherent domains within chimera states.
  • To demonstrate the robustness and versatility of the proposed control strategy.

Main Methods:

  • Utilizing deep reinforcement learning, specifically the soft actor-critic algorithm, to learn control policies.
  • Designing reward functions based on the local order parameter to guide the control of chimera states.
  • Testing the method on both locally coupled Kuramoto oscillators and nonlocally coupled FitzHugh-Nagumo models.

Main Results:

  • The proposed method successfully controls chimera states, confining domains to desired positions, independent of initial conditions and coupling schemes.
  • Demonstrated the ability to generate various chimera patterns, including single-headed, multi-headed, and alternating chimeras, by adjusting control parameters.
  • Showcased the method's universality across different network sizes and its capability to stabilize chimera states against drift and collapse.

Conclusions:

  • Deep reinforcement learning provides a powerful and universal framework for controlling complex dynamical states like chimeras.
  • The model-free nature of the approach enhances its practical applicability to diverse oscillatory systems.
  • This method offers precise spatial control over chimera states, opening new avenues for research and potential applications.