Solitary states in multiplex neural networks: onset and vulnerability

TL;DR

This paper explores how solitary states emerge and persist in multiplex neural networks of FitzHugh-Nagumo neurons, highlighting their robustness and vulnerability to topological changes.

Contribution

It demonstrates the induction of solitary states via weak multiplexing in non-identical layers and analyzes their robustness and vulnerability to topological modifications.

Findings

Solitary states can be induced in fully synchronized networks through weak multiplexing.

The robustness of solitary states is largely independent of initial conditions and inter-layer coupling strength.

Solitary states' survivability depends on network topology and oscillation phase.

Abstract

We investigate solitary states in a two-layer multiplex network of FitzHugh-Nagumo neurons in the oscillatory regime. We demonstrate how solitary states can be induced in a multiplex network consisting of two non-identical layers. More specifically, we show that these patterns can be introduced via weak multiplexing into a network that is fully synchronized in isolation. We show that this result is robust under variations of the inter-layer coupling strength and largely independent of the choice of initial conditions. Moreover, we study the vulnerability of solitary states with respect to changes in the inter-layer topology. In more detail, we remove links that connect two solitary nodes of each layer and evaluate the resulting pattern. We find a highly non-trivial dependence of the survivability of the solitary states on topological (position in the network) and dynamical (phase of the oscillation) characteristics.