Probability of Stability of Synchronization in Random Networks of Mismatched Oscillators

TL;DR

This paper develops a probabilistic framework to analyze the stability of synchronization in networks of mismatched oscillators, providing a generalized master stability function and studying phase transition behavior with numerical validation.

Contribution

It introduces a generalized master stability function accounting for mismatches and derives a lower bound on synchronization probability for various network models.

Findings

Derived a lower bound on synchronization probability

Validated results with numerical examples using van der Pol oscillators

Analyzed the impact of mismatch statistics on synchronization trends

Abstract

The stability of synchronization state in networks of oscillators are studied under the assumption that oscillators and their couplings have slightly mismatched parameters. A generalized master stability function is provided that takes the mismatches into account. Using this master stability function a lower bound on the probability of synchronization is derived for regular and random network models. The probability of stability of synchronization is then used to study the phase transition behavior of the networks. Numerical examples using van der Pol oscillators are used to illustrate the results and verify the validity of the analysis. Moreover, the synchronization trend as a function of statistics of mismatches in the coupling and local dynamics is investigated using this numerical example.