一类具有扩散的捕食-食饵模型正解的存在性和惟一性

Abstract

Abstract:

The predator-prey model with Beddington-DeAngelis functional response is considered. A necessary and sufficient condition for the existence of positive solutions is obtained. Moreover, a range of parameters for the uniqueness of positive solution is described in one dimension. The method used here is based on the global bifurcation theory, the implicit function theorem and the generalized maximum principle.

Key words: Predator-prey, Diffusion, Bifurcation, Uniqueness

CLC Number:

35K57

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GUO Gai-Hui, WU Jian-Hua. Existence and Uniqueness of Positive Solution for a Predator-prey Model with Diffusion[J].Acta mathematica scientia,Series A, 2011, 31(1): 196-205.

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References

[1] Dimitrov D T, Kojouharov H V. Complete mathematical analysis of predator-prey models with linear prey growth and Beddington-DeAngelis functional response. Appl Math Comput, 2005, 162(2): 523--538

[2] Blat J, Brown K J. Global bifurcation of positive solutions in some systems of elliptic equations. SIAM J Math Anal, 1986, 17(6): 1339--1353

[3] Lòpez-Gòmez J, Pardo R. Existence and uniqueness of coexistence states for the predator-prey Lotka-Volterra model with diffusion on intervals. Differential Integral Equations, 1993, 6(5): 1025--1031

[4] 郭改慧, 吴建华. 一类捕食-食饵模型正解的存在性和惟一性. 武汉大学学报(理学版), 2008, 54(1): 9--14

[5] 郭改慧, 李艳玲. 带B-D反应项的捕食-食饵模型的全局分支及稳定性. 应用数学学报, 2008, 31(2): 320--330

[6] Guo G H, Wu J H. Multiplicity and uniqueness of positive solutions for a predator-prey model with B-D functional response.
Nonlinear Analysis TMA, 2010, 72: 1632--1646

[7] Chen W Y, Wang M X. Qualitative analysis of predator-prey models with Beddington-DeAngelis functional response and diffusion. Mathematical and Computer Modelling, 2005, 42: 31--44

[8] 叶其孝, 李正元. 反应扩散方程引论. 北京: 科学出版社, 1994

[9] Smoller J. Shock Waves and Reaction-diffusion Equations. New York: Springer-Verlag, 1999: 167--180

[10] Cantrell R S, Cosner C. On the steady-state problem for the Lotka-Volterra competition model with diffusion. Houston J math, 1987, 13(3): 337--352

[11] Casal A, Eilbeck J C, Lòpez-Gòmez J. Existence and uniqueness of coexistence states for a predator-prey model with diffusion. Differential Integral Equations, 1994, 7(2): 411--439

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Existence and Uniqueness of Positive Solution for a Predator-prey Model with Diffusion

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