Solitary states in arrays of excitable FitzHugh-Nagumo units

Abstract

While coherence-incoherence patterns have been exhaustively studied in systems of coupled oscillators, their mechanisms of emergence and their relationship en route from complete coherence to incoherence in coupled excitable systems remain as yet unresolved. Here we disclose two types of solitary states in arrays of non-locally coupled excitable FitzHugh-Nagumo units with dominant repulsive over attractive interactions. While the prevailing type of solitary states is shown to derive its dynamical features from unbalanced two-cluster states in globally coupled networks, the minority type is fundamentally a consequence of non-locality of interactions. Apart from the states whose local structure is based on successive spiking of units, we also find solitary states where local excitability and slow-fast dynamics give rise to leap-frog activity characterized by an alternating order of units’ spiking. The main impact of noise on system’s behavior is shown to be the reduction of its multistability, whereby the solitary states are suppressed in favour of patched patterns.