Theory of synchronisation and pattern formation on time varying networks

TL;DR

This paper extends the master stability formalism to analyze synchronization and pattern formation on networks that change over time, providing a general theoretical framework validated through specific examples.

Contribution

It introduces a comprehensive extension of the master stability formalism to time-varying networks, overcoming previous limitations and assumptions.

Findings

Successfully applied to synchronization and Turing pattern scenarios

Demonstrates the formalism's robustness across different network dynamics

Provides a unified theoretical approach for evolving networks

Abstract

Synchronisation and pattern formation have been intensely addressed for systems evolving on static networks. Extending the study to include the inherent ability of the network to adjust over time proved cumbersome and led to conclusions which lack of generality, as relying on peculiar assumptions. Here, the master stability formalism is extended to account, in a thoroughly general prospect, for the additional contributions as stemming from the time evolution of the underlying network. The theory is successfully challenged against two illustrative testbeds, which can be respectively ascribed to synchronisation and Turing settings.