The existence, bifurcation and stability of positive stationary solutions of a diffusive Leslie-Gower predator-prey model with Holling-type II functional responses

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• 作者：Jun Zhou^a ; ^b ; ^{jzhouwm@gmail.com} ; Junping Shi^b ; ^{shij@math.wm.edu} ; ^{jxshix@wm.edu}
• 关键词：Leslie&ndash ; Gower predator&ndash ; prey model ; Positive steady state solutions ; Multiplicity ; Uniqueness ; Stability
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2013
• 出版时间：15 September, 2013
• 年：2013
• 卷：405
• 期：2
• 页码：618-630
• 全文大小：829 K

文摘

In this paper, we revisit a diffusive Leslie-Gower predator-prey model with Holling-type II functional responses and Dirichlet boundary condition. It is shown that multiple positive steady state solutions exist under certain conditions on the parameters, while for another parameter region, the positive steady state solution is unique and locally asymptotically stable. Results are proved by using bifurcation theory, fixed point index theory, energy estimates and asymptotic behavior analysis.