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Area of Science:

  • Complex Systems
  • Network Science
  • Control Theory

Background:

  • Spontaneous synchronization is a widespread phenomenon in natural and artificial systems.
  • Pulse-coupled oscillators (PCOs) are a standard model for studying synchronization.
  • Current analytical methods for PCOs require ideal conditions (uniform frequencies, no delays, specific initial phases/topologies).

Purpose of the Study:

  • To develop an optimal pulse-interaction mechanism for robust synchronization in PCOs.
  • To overcome limitations of existing analytical models for PCO synchronization.
  • To create a universally applicable phase response function for diverse network conditions.

Main Methods:

  • Utilized reinforcement learning (RL) to discover an optimal phase response function (PRF).
  • Investigated PCO synchronization under non-ideal conditions (heterogeneous frequencies, propagation delays).
  • Derived a heuristic formula for effective PRFs applicable to general networks and initial conditions.

Main Results:

  • An RL-optimized PRF significantly enhances synchronization probability under non-ideal conditions.
  • The proposed heuristic formula provides effective PRFs for small heterogeneities and delays.
  • The developed PRFs are adaptable to various network topologies and initial phase distributions.

Conclusions:

  • Reinforcement learning offers a powerful approach to designing robust synchronization mechanisms for PCOs.
  • The heuristic formula provides a practical method for optimizing PCO synchronization without network-specific retraining.
  • This work advances the understanding and application of synchronization in complex systems.