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Pattern formation for reactive species undergoing anisotropic diffusion

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Listed:
  • Daniel M. Busiello
  • Gwendoline Planchon
  • Malbor Asllani
  • Timoteo Carletti
  • Duccio Fanelli

Abstract

Turing instabilities for a two species reaction-diffusion system is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive. Under this working hypothesis, the conditions for the onset of the instability are mathematically derived and numerically validated. Patterns which closely resemble those obtained in the classical context of isotropic diffusion, develop when the usual Turing condition is violated, along one of the two accessible directions of migration. Remarkably, the instability can also set in when the activator diffuses faster than the inhibitor, along the direction for which the usual Turing conditions are not matched. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurphb:v:88:y:2015:i:9:p:1-7:10.1140/epjb/e2015-60269-0
    DOI: 10.1140/epjb/e2015-60269-0
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    Cited by:

    1. 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.

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    Statistical and Nonlinear Physics;

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