Pattern formation for reactive species undergoing anisotropic diffusion

Daniel M. Busiello, Gwendoline Planchon, Malbor Asllani, Timoteo Carletti, Duccio Fanelli

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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.
Original languageEnglish
Pages (from-to)222
Number of pages7
JournalEuropean Physical Journal B
Issue number222
Publication statusPublished - 1 Sep 2015


  • dynamical systems
  • Turing patterns
  • reaction diffusion
  • anisotropic diffusion


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