Dynamics of prey-predator -species models with density dependent diffusion

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• 作者：Yujuan Chen ^{nttccyj@ntu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Predator&ndash ; prey models ; Degenerate diffusion ; Ratio-dependent reaction ; Dynamical behavior ; Global attractor ; Stability
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：72
• 期：6
• 页码：1727-1742
• 全文大小：2771 K

文摘

This paper is concerned with the n$n$-species predator–prey models in a bounded domain in two cases, one of which involves n−1$n-1$ cooperative preys and the other involves n−1$n-1$ competitive preys. In these models, the diffusion coefficients may be density dependent, and the reaction functions include ratio-dependent terms. Some simple conditions are obtained to ensure the dynamical behaviors of the time-dependent solutions in relation to some positive solutions or quasi-solutions of the steady-state problems, which include the existence of these solutions. This dynamical behaviors lead to the coexistence and global attractors of the predator–prey systems. Some numerical simulations are given in the end.