Propagation of extreme events in multiplex neuronal networks

TL;DR

This study investigates how extreme events propagate between layers in multiplex neuronal networks, revealing that unidirectional coupling can induce and bidirectional coupling can reduce such events, with implications for understanding real-world network dynamics.

Contribution

It extends previous work by analyzing interlayer propagation of extreme events in multiplex networks with FitzHugh-Nagumo neurons, highlighting the effects of coupling directionality.

Findings

Unidirectional coupling induces extreme events in the uncoupled layer.

Bidirectional coupling mitigates extreme events in the globally coupled layer.

Extreme events emerge through transition from disorder to synchronized activity.

Abstract

In previous studies, the propagation of extreme events across nodes in monolayer networks has been extensively studied. In this work, we extend this investigation to explore the propagation of extreme events between two distinct layers in a multiplex network. We consider a two-layer network, where one layer is globally coupled and exhibits extreme events, while the second layer remains uncoupled. The interlayer connections between the layers are either unidirectional or bidirectional. We find that unidirectional coupling between the layers can induce extreme events in the uncoupled layer, whereas bidirectional coupling tends to mitigate extreme events in the globally coupled layer. To characterize extreme and non-extreme states, we use probability plots to identify distinct regions in the parameter space. Additionally, we study the robustness of extreme events emergence by examining various network topologies in the uncoupled layer. The mechanism behind the occurrence of extreme events is explored, with a particular focus on the transition from asynchronous states to a fully synchronized excitable state. For numerical simulations, we use nonidentical FitzHugh-Nagumo neurons at each node, which captures the dynamical behavior of both coupled and uncoupled layers. Our findings suggest that extreme events in the uncoupled layer emerge through the gradual disappearance of disorder, accompanied by occasional bursts of synchronized activity. Results obtained in this work will serve a starting point in understanding the dynamics behind the propagation of extreme events in real-world networks.