Hopf bifurcation and stability for predator-prey systems with Beddington-DeAngelis type functional response and stage structure for prey incorporating refuge

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• 作者：Fengying Wei ; ^{weifengying@fzu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Qiuyue Fu ^{245060584@qq.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hopf bifurcation ; Predator&ndash ; prey model ; Delay ; Beddington&ndash ; DeAngelis functional response ; Refuge
• 刊名：Applied Mathematical Modelling
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：40
• 期：1
• 页码：126-134
• 全文大小：562 K

文摘

A kind of stage-structured predator–prey model with Beddington–DeAngelis functional response incorporating a prey refuge is investigated in this paper. By analyzing the corresponding characteristic equations, the local stability of the equilibria is investigated. Moreover, Hopf bifurcations occur at the positive equilibrium as the delay pan id="mmlsi12" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0307904X15003534&_mathId=si12.gif&_user=111111111&_pii=S0307904X15003534&_rdoc=1&_issn=0307904X&md5=1b90f07b3b5e1858f990b13ab01334cc" title="Click to view the MathML source">τpan>pan class="mathContainer hidden">pan class="mathCode">$\tau$pan>pan>pan> crosses some critical values. Further, the influence of prey refuge on densities of predator species and prey species is investigated. Numerical simulations are carried out to illustrate our main results.