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Event-triggered feedback in noise-driven phase oscillators.

Justus A Kromer1, Benjamin Lindner2, Lutz Schimansky-Geier2

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Summary
This summary is machine-generated.

Event-triggered feedback in nonlinear phase oscillators significantly alters interevent interval statistics. Both positive and negative feedback can enhance output regularity and influence correlations, with optimal strengths yielding the most pronounced effects.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Statistical physics

Background:

  • Nonlinear phase oscillators are fundamental models in various scientific fields.
  • Understanding event-triggered feedback is crucial for analyzing complex system dynamics.
  • Previous studies have explored oscillatory and excitable regimes but lacked detailed feedback analysis.

Purpose of the Study:

  • To investigate the impact of event-triggered feedback on interevent interval statistics in a nonlinear phase oscillator model.
  • To analyze how positive and negative feedback influence system dynamics, excitability, and noise-induced phenomena.
  • To characterize serial correlations in interevent intervals under different feedback conditions.

Main Methods:

  • Stochastic nonlinear phase oscillator model simulation.
  • Analysis of interevent interval statistics and event-triggered feedback mechanisms.
  • Investigation of saddle node on invariant circle bifurcation and its relation to feedback.
  • Derivation of approximations for the serial correlation coefficient.

Main Results:

  • Positive feedback can induce bistable dynamics and alter system excitability.
  • Both feedback types can regularize output and affect coherence/anticoherence resonance.
  • Positive feedback leads to extended positive interval correlations; negative feedback yields short-ranging negative correlations.
  • Correlations are maximized at optimal feedback strengths near the bifurcation.

Conclusions:

  • Event-triggered feedback introduces significant, tunable control over nonlinear oscillator dynamics.
  • Feedback mechanisms can modulate noise sensitivity and introduce distinct correlation patterns.
  • The study provides a framework for understanding feedback control in complex oscillatory systems.