Global asymptotic stability of a ratio-dependent predator-prey system with diffusion

Authors:
Yong-Hong Fan;Wan-Tong Li
Affiliations:
College of Mathematics and Information Science, Northwest Normal University, Lanzhou, People's Republic of China and School of Mathematics and Statistics, Lanzhou University, Lanzhou, People's Rep ...;School of Mathematics and Statistics, Lanzhou University, Lanzhou, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 2
Cited 2

Global analyses in some delayed ratio-dependent predator-prey systems

Nonlinear Analysis: Theory, Methods & Applications
Periodic solutions and permanence for a delayed nonautonomous ratio-dependent predator-prey model with Holling type functional response

Journal of Computational and Applied Mathematics

Numerical solutions of a Michaelis--Menten-type ratio-dependent predator--prey system with diffusion

Applied Numerical Mathematics
Global solutions to a class of multi-species reaction-diffusion systems with cross-diffusions arising in population dynamics

Journal of Computational and Applied Mathematics

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Abstract

This paper is concerned with a predator-prey system with diffusion. The global asymptotic stability of the unique positive constant equilibrium is obtained under certain conditions. The method used here is the upper and lower solutions combined with the monotone iteration and constructing suitable Lyapunov functions.