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 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
Volume7
Edition15
Publication statusPublished - 6 Jul 2015

Publication series

NamenaXys Technical Report Series
PublisherUniversity of Namur
No.15
Volume7

Fingerprint

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

Keywords

  • 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.
Petit, Julien ; Carletti, Timoteo ; Asllani, Malbor ; Fanelli, Duccio. / Delay induced Turing-like waves for one species reaction–diffusion model on a network. 15 ed. Namur center for complex systems, 2015. 9 p. (naXys Technical Report Series; 15).
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abstract = "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.",
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Petit, J, Carletti, T, Asllani, M & Fanelli, D 2015, Delay induced Turing-like waves for one species reaction–diffusion model on a network. naXys Technical Report Series, no. 15, vol. 7, vol. 7, 15 edn, Namur center for complex systems.

Delay induced Turing-like waves for one species reaction–diffusion model on a network. / Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio.

15 ed. Namur center for complex systems, 2015. 9 p. (naXys Technical Report Series; Vol. 7, No. 15).

Research output: Book/Report/JournalOther report

TY - BOOK

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N2 - 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.

AB - 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.

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KW - delay differential equations

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Petit J, Carletti T, Asllani M, Fanelli D. Delay induced Turing-like waves for one species reaction–diffusion model on a network. 15 ed. Namur center for complex systems, 2015. 9 p. (naXys Technical Report Series; 15).