Pattern formation for reactive species undergoing anisotropic diffusion

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

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Abstract

Turing instabilities for a two species reaction-diffusion systems 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
PublisherNamur center for complex systems
Number of pages9
Volume3
Edition15
Publication statusPublished - 1 Apr 2015

Publication series

NamenaXys Technical Report Series
PublisherUniversity of Namur
No.15
Volume3

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Keywords

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

Cite this

Busiello, D. M., Planchon, G., Asllani, M., Carletti, T., & Fanelli, D. (2015). Pattern formation for reactive species undergoing anisotropic diffusion. (15 ed.) (naXys Technical Report Series; Vol. 3, No. 15). Namur center for complex systems.