Turing patterns in a network-reduced FitzHugh-Nagumo model

Abstract

Reduction of a two-component FitzHugh-Nagumo model to a single-component model with long-range connection is considered on general networks. The reduced model describes a single chemical species reacting on the nodes and diffusing across the links of a multigraph with weighted long-range connections that naturally emerge from the adiabatic elimination, which defines a new class of networked {dynamical} systems with local and nonlocal Laplace matrices. We study the conditions for the instability of homogeneous states in the original and reduced models and show that Turing patterns can emerge in both models.

References in corpus (12)

• Turing patterns in network-organized activator-inhibitor systems
• Turing patterns on networks
• Topology-driven instabilities: the theory of pattern formation on directed networks
• Pattern formation in multiplex networks
• Turing patterns in multiplex networks
• The theory of Turing patterns on time varying networks
• Patterns of non-normality in networked systems
• Instability of Turing patterns in reaction-diffusion-ODE systems
• Drifting Pattern Domains in a Reaction-Diffusion System with Nonlocal Coupling
• Pattern formation in a two-component reaction-diffusion system with delayed processes on a network
• Dynamics of reaction-diffusion patterns controlled by asymmetric nonlocal coupling as limiting case of differential advection
• Spike patterns in a reaction-diffusion-ode model with Turing instability

Cited by in corpus (6)

• Turing patterns on discrete topologies: from networks to higher-order structures
• Turing instability in quantum activator-inhibitor systems
• Spatiotemporal instabilities and pattern formation in systems of diffusively coupled Izhikevich neurons
• Turing patterns on polymerized membranes: a coarse-grained lattice modelling with internal degree of freedom for polymer direction
• Finite propagation enhances Turing patterns in reaction-diffusion networked systems
• Bumps, chimera states, and Turing patterns in systems of coupled active rotators