Bifurcation Behaviors Analysis on a Predator---Prey Model with Nonlinear Diffusion and Delay

Authors:
Changjin Xu;Peiluan Li
Affiliations:
Guizhou Key Laboratory of Economics System Simulation, Guizhou Universityof Finance and Economics, Guiyang, People's Republic of China;Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, People's Republic of China
Venue:
Journal of Dynamical and Control Systems
Year:
2014

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Abstract

In this paper, a class of predator---prey model with nonlinear diffusion and time delay is considered. The stability is investigated and Hopf bifurcation is demonstrated. Applying the normal form theory and the center manifold argument, we derive the explicit formulas for determining the properties of the bifurcating periodic solutions. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, main conclusions are included.