Qualitative analysis on a diffusive prey-predator model with ratio-dependent functional response  

作　　者：PENG Rui WANG MingXin 

机构地区：[1]Institute of Nonlinear Complex Systems,College of Science,China Three Gorges University,Yichang 443002,China [2]Department of Mathematics,Southeast University,Nanjing 210018,China

出　　处：《Science China Mathematics》2008年第11期2043-2058,共16页中国科学：数学（英文版）

基　　金：the National Natural Science Foundation of China (Grant Nos. 10801090, 10726016,10771032);the Scientific Innovation Team Project of Hubei Provincial Department of Education (Grant No.T200809)

摘　　要：In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steadystates if the diffusion rates are large or small.

关 键 词：a prey-predator model DIFFUSION RATIO-DEPENDENT STEADY-STATE global stability NON-EXISTENCE 35J55 37B25 92D25 

分 类 号：Q141[生物学—生态学]