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 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.

Original languageEnglish
Article number58002
Number of pages9
JournalEurophysics Letters
Issue number5
Publication statusPublished - 18 Sept 2015


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


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