Pattern formation in multiplex networks

Abstract

The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the classical continuous media. Here we study pattern formation in a new framework, namely multiplex networks. These are systems where activator and inhibitor species occupy separate nodes in different layers. Species react across layers but diffuse only within their own layer of distinct network topology. This multiplicity generates heterogeneous patterns with significant differences from those observed in single-layer networks. Remarkably, diffusion-induced instability can occur even if the two species have the same mobility rates; condition which can never destabilize single-layer networks. The instability condition is revealed using perturbation theory and expressed by a combination of degrees in the different layers. Our theory demonstrates that the existence of such topology-driven instabilities is generic in multiplex networks, providing a new mechanism of pattern formation.

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Cited by in corpus (43)

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• Multilayer Networks in a Nutshell
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• Inter-layer synchronization in multiplex networks
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• The theory of Turing patterns on time varying networks
• Weak multiplexing in neural networks: Switching between chimera and solitary states
• Master stability functions reveal diffusion-driven pattern formation in networks
• Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network
• Multilayer Network Science: from Cells to Societies
• Optimal self-induced stochastic resonance in multiplex neural networks: electrical versus chemical synapses
• Assessing diversity in multiplex networks
• Diffusive behavior of multiplex networks
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• Turing instability in Reaction-Diffusion models on complex networks
• Tune the topology to create or destroy patterns
• Turing patterns on discrete topologies: from networks to higher-order structures
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• Optimization of synchronizability in multiplex networks by rewiring one layer
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• Benjamin-Feir instabilities on directed networks
• Global topological control for synchronized dynamics on networks
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• Prime stars multiplexes
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