Pattern formation for reactive species undergoing anisotropic diffusion

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

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Résumé

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
langue originaleAnglais
EditeurNamur center for complex systems
Nombre de pages9
Volume3
Edition15
étatPublié - 1 avr. 2015

Série de publications

NomnaXys Technical Report Series
EditeurUniversity of Namur
Numéro15
Volume3

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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, Numéro 15). Namur center for complex systems.
Busiello, Daniel M. ; Planchon, Gwendoline ; Asllani, Malbor ; Carletti, Timoteo ; Fanelli, Duccio. / Pattern formation for reactive species undergoing anisotropic diffusion. 15 Ed. Namur center for complex systems, 2015. 9 p. (naXys Technical Report Series; 15).
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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, theinstability can also set in when the activator diffuses faster than the inhibitor, along the direction for which the usual Turing conditions are not matched",
keywords = "dynamical systems, Turing patterns, reaction diffusion, anisotropic diffusion",
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Busiello, DM, Planchon, G, Asllani, M, Carletti, T & Fanelli, D 2015, Pattern formation for reactive species undergoing anisotropic diffusion. naXys Technical Report Series, Numéro 15, VOL. 3, VOL. 3, 15 edn, Namur center for complex systems.

Pattern formation for reactive species undergoing anisotropic diffusion. / Busiello, Daniel M.; Planchon, Gwendoline; Asllani, Malbor; Carletti, Timoteo; Fanelli, Duccio.

15 Ed. Namur center for complex systems, 2015. 9 p. (naXys Technical Report Series; Vol 3, Numéro 15).

Résultats de recherche: Livre/Rapport/RevueAutre rapport

TY - BOOK

T1 - Pattern formation for reactive species undergoing anisotropic diffusion

AU - Busiello, Daniel M.

AU - Planchon, Gwendoline

AU - Asllani, Malbor

AU - Carletti, Timoteo

AU - Fanelli, Duccio

PY - 2015/4/1

Y1 - 2015/4/1

N2 - 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, theinstability can also set in when the activator diffuses faster than the inhibitor, along the direction for which the usual Turing conditions are not matched

AB - 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, theinstability can also set in when the activator diffuses faster than the inhibitor, along the direction for which the usual Turing conditions are not matched

KW - dynamical systems

KW - Turing patterns

KW - reaction diffusion

KW - anisotropic diffusion

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Busiello DM, Planchon G, Asllani M, Carletti T, Fanelli D. Pattern formation for reactive species undergoing anisotropic diffusion. 15 Ed. Namur center for complex systems, 2015. 9 p. (naXys Technical Report Series; 15).