Delay induced Turing-like waves for one species reaction-diffusion model on a network

Abstract

A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an external non homogenous perturbation. These are generalized Turing-like waves that materialize in a single species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time delayed differential equation. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz networks and with the inclusion of the delay.

References in corpus (5)

• Turing patterns in network-organized activator-inhibitor systems
• Delays, connection topology, and synchronization of coupled chaotic maps
• Pattern formation in multiplex networks
• Total and partial amplitude death in networks of diffusively coupled oscillators
• Synchronizability of chaotic logistic maps in delayed complex networks

Cited by in corpus (4)

• Pattern formation in a two-component reaction-diffusion system with delayed processes on a network
• Turing patterns on discrete topologies: from networks to higher-order structures
• Global topological control for synchronized dynamics on networks
• Networks of planar Hamiltonian systems