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 (27)

• Multilayer Networks
• The structure and dynamics of multilayer networks
• Chimera States for Coupled Oscillators
• When Nonlocal Coupling Between Oscillators Becomes Stronger: Patched Synchrony or Multi-Chimera States
• Chimera states in brain networks: empirical neural vs. modular fractal connectivity
• Solitary state at the edge of synchrony in ensembles with attractive and repulsive interaction
• FitzHugh-Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena
• Solitary states for coupled oscillators
• Time-delayed feedback control of coherence resonance chimeras
• Birth and Death of Chimera: Interplay of Delay and Multiplexing
• Weak multiplexing in neural networks: Switching between chimera and solitary states
• Emergence of chimera in multiplex network
• Solitary states in adaptive nonlocal oscillator networks
• Partial Synchronization and Partial Amplitude Death in Mesoscale Network Motifs
• Non-identical multiplexing promotes chimera states
• Synchronization Patterns: From Network Motifs to Hierarchical Networks
• Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi maps
• Delay-induced chimeras in neural networks with fractal topology
• Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators
• Delay engineered solitary states in complex networks
• The Boundaries of Synchronization in Oscillators Networks
• Chimera and solitary states in 3D oscillator networks with inertia
• Real-time vulnerability of synchronized states
• Spiral wave chimeras for coupled oscillators with inertia
• Solitary states in the mean-field limit
• Taming Chimeras in Networks through Multiplexing Delays
• Dynamics of a 2D lattice of van der Pol oscillators with nonlinear repulsive coupling

Cited by in corpus (12)

• Does the brain behave like a (complex) network? I. Dynamics
• Unbalanced clustering and solitary states in coupled excitable systems
• Asymmetry-induced order in multilayer networks
• Multiplexing-based control of stochastic resonance
• Transition from chimera/solitary states to traveling waves
• Solitary routes to chimera states
• Mixed-Mode Chimera states in Pendula Networks
• 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