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Pattern formation in a two-component reaction–diffusion system with delayed processes on a network

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  • Petit, Julien
  • Asllani, Malbor
  • Fanelli, Duccio
  • Lauwens, Ben
  • Carletti, Timoteo

Abstract

Reaction–diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us to get explicit analytic conditions for the onset of patterns as a function of the main involved parameters, the time-delay, the network topology and the diffusion coefficients. Depending on these parameters, the analysis predicts whether the system will evolve towards a stationary Turing pattern or rather to a wave pattern associated to a Hopf bifurcation. The possible outcomes of the linear analysis overcome the respective limitations of the single-species case with delay, and that of the classical activator–inhibitor variant without delay. Numerical results gained from the Mimura–Murray model support the theoretical approach.

Suggested Citation

  • Petit, Julien & Asllani, Malbor & Fanelli, Duccio & Lauwens, Ben & Carletti, Timoteo, 2016. "Pattern formation in a two-component reaction–diffusion system with delayed processes on a network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 230-249.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:230-249
    DOI: 10.1016/j.physa.2016.06.003
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    References listed on IDEAS

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    1. Daniel M. Busiello & Gwendoline Planchon & Malbor Asllani & Timoteo Carletti & Duccio Fanelli, 2015. "Pattern formation for reactive species undergoing anisotropic diffusion," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(9), pages 1-7, September.
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    Cited by:

    1. Tian, Canrong & Ling, Zhi & Zhang, Lai, 2020. "Delay-driven spatial patterns in a network-organized semiarid vegetation model," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Bao, Xiaomei & Tian, Canrong, 2019. "Delay driven vegetation patterns of a plankton system on a network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 74-88.

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