Pattern analysis of a modified Leslie-Gower predator-prey model with Crowley-Martin functional response and diffusion

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• 作者：Hongwei Yin ; ^{hongwei-yin@hotmail.com" class="auth_mail} ; Xiaoyong Xiao ; Xiaoqing Wen ; Kai Liu
• 关键词：Modified Leslie&ndash ; Gower predator&ndash ; prey model ; Crowley&ndash ; Martin functional response ; Global solution ; Qualitative analysis ; Positive steady states
• 刊名：Computers and Mathematics with Applications
• 出版年：May, 2014
• 年：2014
• 卷：67
• 期：8
• 页码：1607-1621
• 全文大小：412 K

文摘

In this paper, we study a modified Leslie-Gower predator-prey model with Crowley-Martin functional response and spatial diffusion under homogeneous Neumann boundary condition, and obtain some important qualitative properties, including the existence of the global positive solution, the dissipation and persistence of the two species, the local and global asymptotic stability of the constant equilibria, and Hopf bifurcation around the interior constant equilibrium. In addition, we establish the existence and nonexistence of nonconstant positive steady states.