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The Scientific World Journal
Volume 2014, Article ID 721403, 10 pages
http://dx.doi.org/10.1155/2014/721403
Research Article

Dynamics of a Diffusive Predator-Prey Model with General Nonlinear Functional Response

School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, China

Received 7 August 2013; Accepted 13 November 2013; Published 3 February 2014

Academic Editors: M. Bellassoued, J. Fernández, and J.-L. Liu

Copyright © 2014 Wensheng Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a diffusive predator-prey model with nonconstant death rate and general nonlinear functional response. Firstly, stability analysis of the equilibrium for reduced ODE system is discussed. Secondly, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. Furthermore, sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using the method of Lyapunov function. Finally, we show that there are no nontrivial steady state solutions for certain parameter configuration.