Solitary states in multiplex neural networks: onset and vulnerability

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.

References in corpus (8)

• The structure and dynamics of multilayer networks
• FitzHugh-Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena
• Non-identical multiplexing promotes chimera states
• Partial Synchronization and Partial Amplitude Death in Mesoscale Network Motifs
• Synchronization Patterns: From Network Motifs to Hierarchical Networks
• Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators
• Solitary states in the mean-field limit
• Dynamics of a 2D lattice of van der Pol oscillators with nonlinear repulsive coupling

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• Solitary states in complex networks: impact of topology
• Multiplexing-based control of wavefront propagation: the interplay of inter-layer coupling, asymmetry and noise
• Sparsity-driven synchronization in oscillators networks
• Chimera states for directed networks
• Edges of inter-layer synchronization in multilayer networks with time-switching links