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

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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.

Original languageEnglish
Article number58002
Number of pages9
JournalEurophysics Letters
Volume111
Issue number5
Publication statusPublished - 18 Sep 2015

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direct numerical simulation
traveling waves
dynamic models
broken symmetry
differential equations
time lag
inclusions
perturbation
predictions

Keywords

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

Cite this

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title = "Delay induced Turing-like waves for one species reaction–diffusion model on a network",
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.",
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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, Vol. 111, No. 5, 58002, 18.09.2015.

Research output: Contribution to journalArticle

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