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

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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.
Original languageEnglish
PublisherNamur center for complex systems
Number of pages9
Publication statusPublished - 6 Jul 2015

Publication series

NamenaXys Technical Report Series
PublisherUniversity of Namur



  • nonlinear absorption
  • spatio-temporal patterns
  • Complex Networks
  • delay differential equations
  • Turing waves

Cite this

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.