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November  2006, 6(6): 1321-1338. doi: 10.3934/dcdsb.2006.6.1321

On the dynamics of a ratio dependent Predator-Prey system with diffusion and delay

Marcos Lizana 1, and  Julio Marín 2,

1. 

Departamento de Matemáticas, Facultad de Ciencias, Universidad de los Andes, Mérida, Venezuela
2. 

Departamento de Matemática, Escuela de Ciencias, Núcleo de Sucre, Universidad de Oriente, Av. Universidad, Cumaná, Edo. Sucre, Venezuela

Received  May 2005 Revised  June 2006 Published  August 2006

The main concern of this paper is to study the dynamic of a ratio dependent predator-prey system with diffusion and delay. Concretely, we study the dissipativeness and persistence of the system. We show that there are no non trivial steady states solutions for certain parameter's configuration; and discuss the existence of attracting periodic solutions.
Keywords: persistence. Ratio-dependent predator-prey. Reaction-diffusion system.Attracting periodic orbit., Dissipation.
Mathematics Subject Classification: Primary: 92D25; Secondary: 35K5.
Citation: Marcos Lizana, Julio Marín. On the dynamics of a ratio dependent Predator-Prey system with diffusion and delay. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1321-1338. doi: 10.3934/dcdsb.2006.6.1321
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