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January/February 2011 Nonlinear diffusion effect on bifurcation structures for a predator-preymodel
Gaihui Guo, Cui Ma, Jianhua Wu
Differential Integral Equations 24(1/2): 177-198 (January/February 2011).

Abstract

We study a nonlinear diffusive predator-prey model with modified Leslie-Gower and Holling-type II functional responses. Making use of global bifurcation theory, we obtain two sufficient conditions for the existence of positive solutions and describe the coexistence region $R$. Moreover, we find that the coexistence region $R$ spreads as $\beta$ increases and narrows for large $\alpha$. At last, we derive the nonlinear effect of large $\beta$ on bifurcation structures in the special case of $\alpha=0$. Some a priori estimates for positive solutions will play an important role in the proof.

Citation

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Gaihui Guo. Cui Ma. Jianhua Wu. "Nonlinear diffusion effect on bifurcation structures for a predator-preymodel." Differential Integral Equations 24 (1/2) 177 - 198, January/February 2011.

Information

Published: January/February 2011
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35267
MathSciNet: MR2759357

Subjects:
Primary: 35K57

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.24 • No. 1/2 • January/February 2011
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