Unbalanced clustering and solitary states in coupled excitable systems

TL;DR

This paper investigates how unbalanced clustering and solitary states emerge in coupled excitable systems with repulsive interactions, revealing their mechanisms and the influence of noise on these states.

Contribution

It uncovers the connection between unbalanced cluster states and solitary states, and explores how excitability and multiscale dynamics lead to complex spiking patterns.

Findings

Solitary states inherit features from unbalanced cluster states.

Noise suppresses multistability and homogenizes patterns.

Leap-frog states involve alternating spiking order.

Abstract

We demonstrate the mechanisms of emergence and the link between two types of symmetry-broken states, the unbalanced periodic two-cluster states and solitary states, in coupled excitable systems with prevalent repulsive interactions. Solitary states in non-locally coupled arrays inherit their dynamical features from unbalanced cluster states in globally coupled networks. Apart from self-organization based on phase-locked synchrony, interplay of excitability and local multiscale dynamics also gives rise to leap-frog states involving alternating order of spiking. Noise suppresses multistability of cluster states and induces pattern homogenization, transforming solitary states into patterns of patched