Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion

Marco Sammartino, Maria Carmela Lombardo, Tulumello, Sammartino, Lombardo

Risultato della ricerca: Articlepeer review

19 Citazioni (Scopus)

Abstract

In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally, when the pattern invades the domain as a travelling wavefront, we derive the Ginzburg-Landau amplitude equation which is able to describe the shape and the speed of the wave.
Lingua originaleEnglish
pagine (da-a)621-633
Numero di pagine13
RivistaActa Applicandae Mathematicae
Volume132
Stato di pubblicazionePublished - 2014

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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