Unbalanced clustering and solitary states in coupled excitable systems

We discover 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 attractive and repulsive interactions. The prevalent solitary states in non-locally coupled arrays, whose self-organization is based on successive (order preserving) spiking of units, derive their dynamical features from the corresponding unbalanced cluster states in globally coupled networks. Apart from the states with successive spiking, we also find cluster and solitary states where the interplay of excitability and local multiscale dynamics gives rise to so-called leap-frog activity patterns with an alternating order of spiking between the units. We show that the noise affects the system dynamics by suppressing the multistability of cluster states and by inducing pattern homogenization, transforming solitary states into patterns of patched synchrony.

Automated summary

In this study, we investigate the mechanisms and connection between two types of symmetry-broken states, the unbalanced periodic two-cluster states and solitary states, in coupled excitable systems with attractive and repulsive interactions. We find that the prevalent solitary states in non-locally coupled arrays derive their dynamic features from the corresponding unbalanced cluster states in globally coupled networks. Additionally, we discover cluster and solitary states with leap-frog activity patterns, where the interplay of excitability and local multiscale dynamics leads to an alternating order of spiking between the units.