一类带非单调转化率的捕食-食饵模型的全局分歧The global bifurcation of a prey-predator model with non-monotone conversion rate
李艳玲;江伟;
摘要(Abstract)：
主要研究了一类带非单调转化率的捕食-食饵模型,分别以生长率α和b为分歧参数,运用度理论和分歧理论讨论了这类模型在齐次第一边界条件下全局分歧结构.
关键词(KeyWords)： 捕食-食饵模型;全局分歧;不动点指标
基金项目(Foundation): 国家自然科学基金(10971124);; 陕西省自然科学基础研究资助项目(2007A11)
作者(Authors): 李艳玲;江伟;
参考文献(References)：
- [1]Blat J,Brown K J.Global bifurcation of positive solutions in some systems of elliptic equations[J].SIAM J. Math.Anal.,1986,17(6):1339-1353.
- [2]Du Y H,Lou Y.Some uniqueness and exact multiplicity results for a predator-prey model[J].Trans.Amer. Math.Soc.,1997,349(6):2443-2475.
- [3]Pang P Y H,Wang M X.Qualitative analysis of a ratio-dependent predator-prey system with diffusion[J]. Proc.Roy.Soc.Edinburgh Sect.A,2003,133(4):919-942.
- [4]Du Y H,Lou Y.S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model[J].J.Differential Equations,1998,144(2):390-440.
- [5]Freedman H I,Wolkowicz G S K.Predator-prey systems with group defense:The paradox of enrichment revisited[J].Bull.Math.Biol.,1986,48(5/6):493-508.
- [6]Pang P Y H,Wang M X.Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion[J].Proc.London Math.Soc.,2004,88(1):135-157.
- [7]Wang M X.Stationary patterns for a prey-predator model with prey-dependent and ratio-dependent functional responses and diffusion[J].Phys.D.,2004,196(1/2):172-192.
- [8]Wang M X.Stationary patterns of strongly coupled prey-predator models[J].J.Math.Anal.Appl.,2004,29 2(2):484-505.
- [9]Murray J D.Mathematical Biology[M].3rd ed.Berlin:Springer,2003.
- [10]Ruan W H,Feng W.On the fixed point index and multiple steady-state solutions of reaction-diffusion systems[J].Differential Integral Equations,1995,8(2):371-391.
- [11]Peng R,Wang M X,Chen W Y.Positive steady states of a prey-predator model with Diffusion and nonmonotone conversion rate[J].Acta Math.Sin.,2007,23(4):749-760.