## Differential and Integral Equations

### Nonlinear diffusion effect on bifurcation structures for a predator-prey model

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 24, Number 1/2 (2011), 177-198.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356019050

Mathematical Reviews number (MathSciNet)
MR2759357

Zentralblatt MATH identifier
1240.35267

Subjects
Primary: 35K57: Reaction-diffusion equations

#### Citation

Wu, Jianhua; Guo, Gaihui; Ma, Cui. Nonlinear diffusion effect on bifurcation structures for a predator-prey model. Differential Integral Equations 24 (2011), no. 1/2, 177--198. https://projecteuclid.org/euclid.die/1356019050