Synchronization of uncoupled oscillators by common gamma impulses: from phase locking to noise-induced synchronization

TL;DR

This paper investigates how uncoupled oscillators synchronize under common gamma-distributed impulses, bridging the gap between phase locking to periodic impulses and noise-induced synchronization from random impulses, using various analytical measures.

Contribution

It provides a unified analysis of synchronization mechanisms driven by gamma-distributed impulses, quantifying differences between phase locking and noise-induced synchronization.

Findings

Gamma-distributed impulses interpolate between periodic and Poisson impulses.

Distinct phase distributions and Lyapunov exponents characterize different synchronization regimes.

Information-theoretic measures reveal clear differences in synchronization dynamics.

Abstract

Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii) noise-induced synchronization caused by Poisson random impulses, but their difference has not been fully quantified. Here we analyze a pair of uncoupled oscillators subject to common random impulses with gamma-distributed intervals, which can be smoothly interpolated between regular periodic and random Poisson impulses. Their dynamics are charac- terized by phase distributions, frequency detuning, Lyapunov exponents, and information-theoretic measures, which clearly reveal the differences between the two synchronization scenarios.