Desynchronization transitions in adaptive networks

TL;DR

This paper develops a master stability framework for adaptive networks, revealing how adaptivity influences synchronization, leading to stability islands and desynchronization transitions, with applications to oscillator and neuron models.

Contribution

It introduces a novel master stability approach for adaptive networks, enabling analysis of synchronization phenomena and uncovering stability islands and desynchronization transitions.

Findings

Identification of stability islands in adaptive networks

Discovery of desynchronization transitions with increased coupling

Application to oscillator and neuron models with synaptic plasticity

Abstract

Adaptive networks change their connectivity with time, depending on their dynamical state. While synchronization in structurally static networks has been studied extensively, this problem is much more challenging for adaptive networks. In this Letter, we develop the master stability approach for a large class of adaptive networks. This approach allows for reducing the synchronization problem for adaptive networks to a low-dimensional system, by decoupling topological and dynamical properties. We show how the interplay between adaptivity and network structure gives rise to the formation of stability islands. Moreover, we report a desynchronization transition and the emergence of complex partial synchronization patterns induced by an increasing overall coupling strength. We illustrate our findings using adaptive networks of coupled phase oscillators and FitzHugh-Nagumo neurons with synaptic plasticity.