Adaptive control of synchronization in delay-coupled heterogeneous networks of FitzHugh-Nagumo nodes

TL;DR

This paper demonstrates that adaptive tuning of coupling strength in delay-coupled FitzHugh-Nagumo networks can restore synchronization despite significant heterogeneity among nodes.

Contribution

It introduces an adaptive control method that counteracts heterogeneity effects, enabling synchronization in diverse neural network models.

Findings

Adaptive tuning restores synchronization in heterogeneous networks.

Synchronization achieved even with large heterogeneity and mixed node dynamics.

Delay-coupled FitzHugh-Nagumo networks can synchronize through adaptive control.

Abstract

We study synchronization in delay-coupled neural networks of heterogeneous nodes. It is well known that heterogeneities in the nodes hinder synchronization when becoming too large. We show that an adaptive tuning of the overall coupling strength can be used to counteract the effect of the heterogeneity. Our adaptive controller is demonstrated on ring networks of FitzHugh-Nagumo systems which are paradigmatic for excitable dynamics but can also -- depending on the system parameters -- exhibit self-sustained periodic firing. We show that the adaptively tuned time-delayed coupling enables synchronization even if parameter heterogeneities are so large that excitable nodes coexist with oscillatory ones.