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.
|Publisher||Namur center for complex systems|
|Number of pages||9|
|Publication status||Published - 6 Jul 2015|
|Name||naXys Technical Report Series|
|Publisher||University of Namur|
- nonlinear absorption
- spatio-temporal patterns
- Complex Networks
- delay differential equations
- Turing waves
Petit, J., Carletti, T., Asllani, M., & Fanelli, D. (2015). Delay induced Turing-like waves for one species reaction–diffusion model on a network. (15 ed.) (naXys Technical Report Series; Vol. 7, No. 15). Namur center for complex systems.