Asymmetric Adaptivity induces Recurrent Synchronization in Complex Networks

TL;DR

This paper introduces a framework explaining how asymmetric adaptation rules in complex networks lead to recurrent synchronization, characterized by alternating coherent and incoherent phases, without altering individual node dynamics.

Contribution

It identifies asymmetric adaptation and temporal separation as key mechanisms for recurrent synchronization in adaptive complex networks.

Findings

Recurrent synchronization manifests as alternating coherent and incoherent episodes.

Asymmetric adaptation rules are crucial for the emergence of this phenomenon.

The dynamics of individual nodes remain qualitatively unchanged during synchronization cycles.

Abstract

Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order to fill this gap, we present a framework for describing the emergence of recurrent synchronization in complex networks with adaptive interactions. This phenomenon is manifested at the macroscopic level by temporal episodes of coherent and incoherent dynamics that alternate recurrently. At the same time, the dynamics of the individual nodes do not change qualitatively. We identify asymmetric adaptation rules and temporal separation between the adaptation and the dynamics of individual nodes as key features for the emergence of recurrent synchronization. Our results suggest that asymmetric adaptation might be a fundamental ingredient for recurrent synchronization phenomena as seen in pattern generators, e.g., in neuronal systems.