On nonlinear coupled diffusions in competition systems

A. El Hamidi, M. Garbey, N. Ali

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

A class of reaction-diffusion systems modeling plant growth with spatial competition in saturated media is presented. We show, in this context, that standard diffusion can not lead to pattern formation (Diffusion Driven Instability of Turing). Degenerated nonlinear coupled diffusions inducing free boundaries and exclusive spatial diffusions are proposed. Local and global existence results are proved for smooth approximations of the degenerated nonlinear diffusions systems which give rise to long-time pattern formations. Numerical simulations of a competition model with degenerate/non degenerate nonlinear coupled diffusions are performed and we carry out the effect of the these diffusions on pattern formation and on the change of basins of attraction.

Original languageEnglish (US)
Pages (from-to)1306-1318
Number of pages13
JournalNonlinear Analysis: Real World Applications
Volume13
Issue number3
DOIs
StatePublished - Jun 2012

Keywords

  • Competition
  • Lyapunov
  • Nonlinear diffusion
  • Pattern formation
  • Turing instability

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

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