Linear and nonlinear stability thresholds for a diffusive model of pioneer and climax species interaction
✍ Scribed by Bruno Buonomo; Salvatore Rionero
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 132 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.1068
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✦ Synopsis
Abstract
In this paper a reaction–diffusion model describing two interacting pioneer and climax species is considered. The role of diffusivity and forcing (stocking or harvesting of the species) on the nonlinear stability of a coexistence equilibrium is analysed. The study is performed in the context of a new approach to nonlinear L^2^‐stability based on the analysis of stability of the zero solution of a suitable linear system of ordinary differential equations. Theorems concerning the effect of forcing and diffusivity on the dynamics are established and stability–instability thresholds for the system are obtained. An example to illustrate the practical use of the results is also provided. Copyright © 2008 John Wiley & Sons, Ltd.