Cross-diffusion driven instability for a Lotka-Volterra competitive reaction-diffusion system

Gambino G; Lombardo M C; Sammartino M

Risultato della ricerca: Paper

Abstract

In this work we investigate the possibility of the pattern formation for a reaction-di®usion system with nonlinear di®usion terms. Through a linear sta- bility analysis we ¯nd the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show how cross-di®usion e®ects are responsible for the initiation of spatial patterns. Finally, we ¯nd a Fisher amplitude equation which describes the weakly nonlinear dynamics of the system near the marginal stability.
Lingua originaleEnglish
Stato di pubblicazionePublished - 2008

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Cross-diffusion driven instability for a Lotka-Volterra competitive reaction-diffusion system. / Gambino G; Lombardo M C; Sammartino M.

2008.

Risultato della ricerca: Paper

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title = "Cross-diffusion driven instability for a Lotka-Volterra competitive reaction-diffusion system",
abstract = "In this work we investigate the possibility of the pattern formation for a reaction-di{\circledR}usion system with nonlinear di{\circledR}usion terms. Through a linear sta- bility analysis we ¯nd the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show how cross-di{\circledR}usion e{\circledR}ects are responsible for the initiation of spatial patterns. Finally, we ¯nd a Fisher amplitude equation which describes the weakly nonlinear dynamics of the system near the marginal stability.",
keywords = "Nonlinear diffusion; Turing pattern formation",
author = "{Gambino G; Lombardo M C; Sammartino M} and Sammartino, {Marco Maria Luigi} and Lombardo, {Maria Carmela} and Gaetana Gambino",
year = "2008",
language = "English",

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TY - CONF

T1 - Cross-diffusion driven instability for a Lotka-Volterra competitive reaction-diffusion system

AU - Gambino G; Lombardo M C; Sammartino M

AU - Sammartino, Marco Maria Luigi

AU - Lombardo, Maria Carmela

AU - Gambino, Gaetana

PY - 2008

Y1 - 2008

N2 - In this work we investigate the possibility of the pattern formation for a reaction-di®usion system with nonlinear di®usion terms. Through a linear sta- bility analysis we ¯nd the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show how cross-di®usion e®ects are responsible for the initiation of spatial patterns. Finally, we ¯nd a Fisher amplitude equation which describes the weakly nonlinear dynamics of the system near the marginal stability.

AB - In this work we investigate the possibility of the pattern formation for a reaction-di®usion system with nonlinear di®usion terms. Through a linear sta- bility analysis we ¯nd the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show how cross-di®usion e®ects are responsible for the initiation of spatial patterns. Finally, we ¯nd a Fisher amplitude equation which describes the weakly nonlinear dynamics of the system near the marginal stability.

KW - Nonlinear diffusion; Turing pattern formation

UR - http://hdl.handle.net/10447/39995

M3 - Paper

ER -