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 (7)

• The theory of Turing patterns on time varying networks
• Diffusive behavior of multiplex networks
• Global topological control for synchronized dynamics on networks
• Self-Organized Stationary Patterns in Networks of Bistable Chemical Reactions
• Relaxation time of the global order parameter on multiplex networks: the role of interlayer coupling in Kuramoto oscillators
• Opinion formation in multiplex networks with general initial distributions
• Coarse-grained patterns in multiplex networks