Turing patterns in multiplex networks

Abstract

The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of an homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations.

References in corpus (5)

• The structure and dynamics of multilayer networks
• Diffusion dynamics on multiplex networks
• Turing patterns in network-organized activator-inhibitor systems
• Transport on coupled spatial networks
• Topology-driven instabilities: the theory of pattern formation on directed networks

Cited by in corpus (7)

• Pattern formation in multiplex networks
• Dynamical Systems on Networks: A Tutorial
• The theory of Turing patterns on time varying networks
• Global topological control for synchronized dynamics on networks
• Relaxation time of the global order parameter on multiplex networks: the role of interlayer coupling in Kuramoto oscillators
• Self-similar Turing Patterns: An Anomalous diffusion consequence
• Coarse-grained patterns in multiplex networks