Synchronization in networks with heterogeneous adaptation rules and applications to distance-dependent synaptic plasticity

TL;DR

This paper develops a methodology to analyze synchronization in adaptive networks with diverse plasticity rules, focusing on phase oscillators with distance-dependent adaptation, and explains how network structure and adaptation influence synchronization.

Contribution

It extends the master stability function approach to heterogeneous adaptive networks, enabling separation of effects from structure, dynamics, and adaptation.

Findings

Long-range connections can induce synchronization or desynchronization.

The methodology explains effects of distance-dependent plasticity on synchronization.

Application to biologically motivated plasticity rules in neural networks.

Abstract

This work introduces a methodology for studying synchronization in adaptive networks with heterogeneous plasticity (adaptation) rules. As a paradigmatic model, we consider a network of adaptively coupled phase oscillators with distance-dependent adaptations. For this system, we extend the master stability function approach to adaptive networks with heterogeneous adaptation. Our method allows for separating the contributions of network structure, local node dynamics, and heterogeneous adaptation in determining synchronization. Utilizing our proposed methodology, we explain mechanisms leading to synchronization or desynchronization by enhanced long-range connections in nonlocally coupled ring networks and networks with Gaussian distance-dependent coupling weights equipped with a biologically motivated plasticity rule.