A PDE model of clonal plant competition with nonlinear diffusion

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• 作者：A. El Hamidi^a ; ^{aelhamid@univ-lr.fr} ; M. Garbey^b ; ^{garbey@cs.uh.edu} ; N. Ali^a ; ^{nali01@univ-lr.fr}
• 关键词：Clonal plant ; Reaction&ndash ; diffusion ; Partial differential equation ; Spatial&ndash ; temporal pattern formation ; Cross diffusion ; Spatial competition
• 刊名：Ecological Modelling
• 出版年：2012
• 期刊代码：49_03043800
• 类别：cp
• 出版时间：10 June, 2012
• 卷：234
• 期：Complete
• 页码：83-92
• 文件大小：2802 K

摘要

We present a spatial competition model for clonal plant growth that combines two different mechanisms of competition. The first one is described by the standard underlying Kolmogorov Model for two interacting populations. A second competition mechanism, more specific to clonal plant growth, expresses the motility of each species and their capacity to resist to competitor's space intrusion. This model leads to a degenerated nonlinear reaction-diffusion system in which the diffusion coefficient of each species vanishes wherever the other species is beyond a certain biomass value.

Indeed, we show that pattern forming instability cannot occur in general competition systems if the exclusion ability of both species is small even if the diffusions are degenerated. The effect of diffusion degeneracy on patterns formation is carried out. Numerical simulations of this two-level competition model are performed when the reaction terms are given by the competitive Lotka-Volterra equations. We, finally, discuss the potential of such nonlinear reaction-diffusion systems to be a surrogate model for phalanx-guerilla species competition.