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.
Delay-induced Turing-like waves for one-species reaction-diffusion model on a network / Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio. - In: EUROPHYSICS LETTERS. - ISSN 0295-5075. - STAMPA. - 111:(2015), pp. 58002-58008. [10.1209/0295-5075/111/58002]
Delay-induced Turing-like waves for one-species reaction-diffusion model on a network
FANELLI, DUCCIO
2015
Abstract
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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.