Mathematical analysis and numerical simulation of pattern formation under cross-diffusion

Ricardo Ruiz-Baier, Canrong Tian

Research output: Contribution to journalArticleResearchpeer-review

49 Citations (Scopus)

Abstract

Cross-diffusion driven instabilities have gained a considerable attention in the field of population dynamics, mainly due to their ability to predict some important features in the study of the spatial distribution of species in ecological systems. This paper is concerned with some mathematical and numerical aspects of a particular reaction-diffusion system with cross-diffusion, modeling the effect of allelopathy on two plankton species. Based on a stability analysis and a series of numerical simulations performed with a finite volume scheme, we show that the cross-diffusion coefficient plays a important role on the pattern selection.

Original languageEnglish
Pages (from-to)601-612
Number of pages12
JournalNonlinear Analysis: Real World Applications
Volume14
Issue number1
DOIs
Publication statusPublished - 1 Feb 2013
Externally publishedYes

Keywords

  • Cross-diffusion
  • Finite volume approximation
  • Pattern formation
  • Pattern selection

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