期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

带有食饵趋向和非单调反应函数捕食模型的稳定性及Hopf分支 被引量：1

Stability and Hopf Bifurcation for a Predator-prey Model with Prey-taxis and Non-monotonic Functional Response
下载PDF
导出
摘要 探讨了一类在齐次留曼边界条件下带有捕食趋向和非单调反应函数捕食模型的稳定性及Hopf分支.证明了在一定条件下当食饵趋向系数充分小时正常数解是全局渐近稳定的,但局部稳定性及其他常数解全局稳定性与食饵趋向系数无关,并证明了该模型有周期解分支. A predator-prey model with prey-taxis incorporating non-monotonic functional response under homogeneous Neumann boundary condition is concerned.The stability and Hopf bifurcation of positive equilibrium points are investigated.The global stability of the positive constant solution is relative to prey-tactic sensitivity coefficient which leads to keep back the global stability,but for the local stability and the global stability of other constant solution,prey-tactic sensitivity coefficient doesn＇t influence on it,and above system has also the periodic bifurcation.
作者 李成林
机构地区 西南大学数学与统计学院 保山学院数学学院
出处 《北华大学学报（自然科学版）》 CAS 2011年第5期505-510,共6页 Journal of Beihua University（Natural Science）
基金 教育部自然科学基金资助项目(20100182110003)
关键词 食饵趋向 稳定 HOPF分支 prey-taxis stability Hopf bifurcation
分类号 O175.1 [理学—基础数学]
  • 相关文献

参考文献15

  • 1A Chakraborty, M Singh, P Ridland. Effect of Prey-taxis on Biological Control of the Two-spotted Spider Mite-A Numerical Approach[J]. Math and Com Mod,2009 ,50 :598-610.
  • 2A Okubo, H C Chiang. An Analysis of the Kinematics of Swarming of Anarete Pritchardi Kim [ J ]. Res Popul Ecol( Kyoto), 1974,16 : 1-42.
  • 3B E Ainseba, M Bendahmane, A Noussair. A Reaction-diffusion System Modeling Predator-prey with Prey-taxis [J]. Nonlinear Anal RWA,2008 ,9 :2086-2105.
  • 4M Bendahmane. Analysis of a Reaction-diffusion System Modeling Predator-prey with Prey-taxis[J]. Net Hetero Med,2008,3: 863 -879.
  • 5Tao. Global Existence of Classical Solutions to a Predator-prey Model with Nonlinear Prey-taxis [ J ]. Nonlinear Anal RWA, 2009,10 : 1016-1112.
  • 6H I Freedman, G S K Wolkowica. Predator-prey Systems with Group Defense :The Paradox of Enrichment Revisited[ J]. Bulletin of Mathematical Biology, 1986,48 (5-6) :493-508.
  • 7G S K Wolkowicz. Bifurcation Analysis of a Predator-prey System Involving Group Defense[ J]. SIAM J, 1988,48:592-606.
  • 8M L Rosenzweig. Paradox of Enrichment: Destabilization of Exploitation Ecosystems in Ecological Time [ J ]. Science, 1969 ( 171 ) :385-387.
  • 9Y H Fan, W T Li. Global Asymptotic Stability of a Ratio-dependent Predator-prey System with Diffusion [ J ]. J Comput Appl Math, 2006,188 : 205-227.
  • 10W Ko, K Ryu. A Qualitative Study on General Cause-type Predator-prey Models with Non-monotonic Functional Response[ J ]. Nonlinear Anal RWA,2009,10:2558-2573.

同被引文献14

  • 1Blat J,Brown K J.Bifurcation of steady-state solutions in predator-prey and competition systems[J].Proc R Edinburgh Sect,1984,A97:21-34.
  • 2Brown K J.Nontrival solutions of predator-prey systems with small diffusions[J].Nonlinear Analysis,1987,11:685-689.
  • 3Hsu S B.On global stability of a predator-prey system[J].Math Biosci,1978,39:1-10.
  • 4Wu jianhua.Coexistence states for cooperative model with diffusion[J].Math Application,2002,43:1277-1290.
  • 5Chen Xinfu,Qi Yuanwei,Wang Mingxin.A strongly coupled predator-prey system with non-monotonic functional response[J].Nonlinear Analysis,2007,67:1966-1979.
  • 6Wonlyul Ko,Kimun Ryu.Coexistence states of a predatorprey system with non-monotonic functional response[J].Nonlinear Analysis,2007,8:769-786.
  • 7Wang Mingxin.Stability and hopf bifurcation for a preypredator model with prey-stage structure and diffurcation[J].Math Boil,2008,212:149-160.
  • 8Ruan S G,Xiao D M.Global analysis in a predator-prey system with nonmonotonic functional response[J].SIAM J Appl Math,2001,61:1445-1472.
  • 9Jia Yunfeng.Coexistence states for cooperative model with diffusion[J].Computers and Mathematics with Application,2002,43:1277-1290.
  • 10Joel S.Shock waves and reaction-diffusion equations[M].New York:Springer-Verlag,1983.

引证文献1

二级引证文献1

北华大学学报（自然科学版）
2011年 第5期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部