A singular perturbation result in competition theory

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• 作者：Sergio Ferná ; ndez-Rinc&oacute ; n ^{sergfern@ucm.es" class="auth_mail" title="E-mail the corresponding author} ; Juliá ; n L&oacute ; pez-G&oacute ; mez ; ^{julian@mat.ucm.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Competition ; Coexistence ; Permanence ; Singular perturbation ; Limiting profiles ; Monotone scheme
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：280-296
• 全文大小：421 K

文摘

This paper establishes a generalized version of the singular perturbation results given by V. Hutson et al. [10, Theorem 4.1] and X. He and W.M. Ni [6, Theorem 4.2 (iii)]. In particular, it ascertains the limiting profiles of the coexistence states of the classical Lotka–Volterra model for two competing species as the diffusion coefficients approximate zero. They are provided by the global attractors of the underlying non-spatial model whenever they exist.