Synchronization of Limit Cycle Oscillators by Telegraph Noise

TL;DR

This paper investigates how telegraph noise affects the synchronization of limit cycle oscillators, deriving explicit Lyapunov exponents and showing conditions for synchronization or desynchronization.

Contribution

It provides an analytical expression for the Lyapunov exponent under telegraph noise and demonstrates its effects on oscillator synchronization and desynchronization.

Findings

Lyapunov exponent is negative for weak or frequent switching noise

Moderate noise can cause desynchronization in certain systems

Phase model accurately predicts behavior under specific noise conditions

Abstract

We study the influence of telegraph noise on synchrony of limit cycle oscillators. Adopting the phase description for these oscillators, we derive the explicit expression for the Lyapunov exponent. We show that either for weak noise or frequent switching the Lyapunov exponent is negative, and the phase model gives adequate analytical results. In some systems moderate noise can desynchronize oscillations, and we demonstrate this for the Van der Pol--Duffing system.