Analysis of parameter mismatches in the master stability function for network synchronization

TL;DR

This paper investigates how small parameter mismatches in network components affect the stability of synchronization, extending the master stability function approach to more realistic, imperfect conditions.

Contribution

It provides a sensitivity analysis of the master stability function for nearly synchronized networks with slight parameter mismatches, addressing practical deviations from ideal synchronization conditions.

Findings

Linear stability is maintained despite small parameter mismatches.

The analysis quantifies the impact of deviations on synchronization stability.

Results are applicable to real-world networks with imperfect conditions.

Abstract

In this letter, we perform a sensitivity analysis on the master stability function approach for the synchronization of networks of coupled dynamical systems. More specifically, we analyze the linear stability of a nearly synchronized solution for a network of coupled dynamical systems, for which the individual dynamics and output functions of each unit are approximately identical and the sums of the entries in the rows of the coupling matrix slightly deviate from zero. The motivation for this parametric study comes from experimental instances of synchronization in human-made or natural settings, where ideal conditions are difficult to observe.