Travelling waves in an ensemble of excitable oscillators: the interplay of memristive coupling and noise

TL;DR

This paper demonstrates how memristive coupling enhances the formation and robustness of travelling waves in an ensemble of excitable oscillators, especially under noisy conditions, using numerical simulations.

Contribution

It reveals the constructive role of memristive coupling in promoting travelling waves at lower coupling strengths and increasing noise resilience in FitzHugh-Nagumo neuron models.

Findings

Memristive coupling enables travelling waves at lower coupling strengths.

Memristive coupling increases the noise threshold for wave destruction.

Lévy noise can induce travelling waves in the system.

Abstract

Using methods of numerical simulation, we demonstrate the constructive role of memristive coupling in the context of the travelling wave formation and robustness in an ensemble of excitable oscillators described by the FitzHugh-Nagumo neuron model. First, the revealed aspects of the memristive coupling action are shown on an example of the deterministic model where the memristive properties of the coupling elements provide for achieving travelling waves at lower coupling strength as compared to non-adaptive diffusive coupling. In the presence of noise, the positive role of memristive coupling is manifested as significant increasing a noise intensity critical value corresponding to the noise-induced destruction of travelling waves as compared to classical diffusive interaction. In addition, we point out the second constructive factor, the L{\'e}vy noise whose properties provide for inducing travelling waves.