Turing instability in Reaction-Diffusion models on complex networks

Abstract

In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erdős-Rényi, the Watts-Strogatz, and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we numerically reveal that stable and unstable regions of a homogeneous steady state on the parameter space of two diffusion coefficients completely differ, depending on the network architecture. In addition, we theoretically discuss the stable and unstable regions in the cases of regular enhanced ring lattices which include regular circles, and networks generated by the threshold network model when the number of vertices is large enough.

Physica A (in press)

References in corpus (13)

• 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
• Spectral distributions of adjacency and Laplacian matrices of random graphs
• Traveling and pinned fronts in bistable reaction-diffusion systems on network
• Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights
• Stochastic Turing Patterns on a Network
• Turing patterns and apparent competition in predator-prey food webs on networks
• Propagation failure of excitation waves on trees and random networks
• Effect of small-world topology on wave propagation on networks of excitable elements
• Excitation Waves on a Minimal Small-World Model

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