Global Stability Analysis of a Ratio-Dependent Predator-Prey System
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摘要: 研究一类基于比率和具第Ⅲ类功能性反应的捕食-食饵系统.通过分析正平衡点的局部稳定性给出了系统正平衡点全局渐近稳定以及系统存在极限环的条件.运用Hopf分支理论讨论了当正平衡点是非双曲型时的情形.Abstract: A ratio dependent predator-prey system with Holling type ó functional response was considered.The sufficient condition of the global asymptotic stability for the positive equilibrium and the existence of the limit cycle were given by studying the locally asymptotic stability of the positive equilibrium.At last,the condition when the positive equilibrium is no hyperbolic equilibrium was discussed by Hopf bifurcation.
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Key words:
- ratio-dependent /
- global asymptotic stability /
- functional response /
- Hopf bifurcation
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[1] Berezovskaya F,Karev G,Arditi R.Parametric analysis of the ratio-dependent predator-prey model[J].J Math Biol,2001,43(3):221-246. doi: 10.1007/s002850000078 [2] XIAO Dong-mei,RUAN Shi-gui.Global dynamics of a ratio-dependent predator-prey system[J].J Math Biol,2001,43(3):268-290. doi: 10.1007/s002850100097 [3] Kuang Y,Beretta E.Global qualitative analysis of a ratio-dependent predator-prey system[J].J Math Biol,1998,36(4):389-406. doi: 10.1007/s002850050105 [4] Hsu S-B,Hwang T-W,Kuang Y.Global analysis of the Michaelis-Menten type ratio-dependent predator-prey system[J].J Math Biol,2001,43(4):221-246. doi: 10.1007/s002850000078 [5] 王琳琳.自治Holling(Ⅲ)类功能性反应的捕食-食饵系统的定性分析[J].西北师范大学学报(自然科学版),2005,41(1):1-6. [6] 鲁铁军,王美娟,刘妍.一类基于比率的捕食-食饵系统的参数分析[J].数学的实践与认识,2007,37(17):98-104. [7] Perko L.Differential Equations and Dynamical Systems[M].2nd Ed.Texts in Applied Mathematics 7.Moscow:Springer-Verlag,1996,344. [8] Guckenheimer J, Holmes P.Nonlinear Oscillation, Dynamical Systems and Bifurcations of Vector Fields[M].New York:Springer-Verlag,1980.
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