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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Most oscillator network studies focus on direct coupling (e.g., Kuramoto model).
  • Indirect coupling via a common medium is increasingly relevant (e.g., bacterial quorum sensing, coupled lasers).
  • Stochastic resetting introduces external environmental perturbations.

Purpose of the Study:

  • To analyze the effects of stochastic phase resetting on a Kuramoto model with indirect coupling.
  • To investigate how collective synchronization is influenced by indirect interactions and environmental resetting.
  • To explore the role of cell density in modulating synchronization dynamics.

Main Methods:

  • Derivation of a continuity equation for population density under stochastic resetting.
  • Application of the Ott-Antonsen (OA) Ansatz to simplify the system.
  • Reduction to a four-dimensional piecewise deterministic system with subsystem resetting.

Main Results:

  • At high densities, OA dynamics with global resetting are recovered, similar to the classical Kuramoto model.
  • At low densities, subsystem resetting significantly alters collective synchronization.
  • Observed phenomena include noise-induced transitions and slow/fast dynamics due to subsystem resetting.

Conclusions:

  • Indirect coupling and stochastic resetting introduce novel dynamics not present in directly coupled systems.
  • Cell density is a critical parameter determining the influence of subsystem resetting on synchronization.
  • The model provides insights into collective behavior in systems like bacterial quorum sensing.