Delay-induced Turing-like waves for one-species reaction-diffusion model on a network
1 naXys, Namur Center for Complex Systems, University of Namur - rempart de la Vierge 8, B 5000 Namur, Belgium
2 Dipartimento di Fisica e Astronomia, University of Florence, INFN and CSDC - Via Sansone 1, 50019 Sesto Fiorentino, Florence, Italy
Received: 8 July 2015
Accepted: 31 August 2015
A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous 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 equations. 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 network and with the inclusion of the delay.
PACS: 89.75.Hc – Networks and genealogical trees / 89.75.Kd – Patterns / 89.75.Fb – Structures and organization in complex systems
© EPLA, 2015