A Note on a Diffusive Predator-prey Model and Its Steady-state System  

作　　者：Rui PENG Ming Xin WANG Guo Ying YANG 

机构地区：[1]Institute of Nonlinear Complex Systems, College of Science, China Three Gorges University, Yichang 443002, P. R. China [2]Department of Mathematics, Southeast University, Nanjing 210096, P. R. China [3]Department of Mathematics, Henan Polytechnic University, Jiaozuo 454100, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第5期963-974,共12页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 10801090, 10871185, 10726016);supported by the Scientifio Research Projects of Hubei Provincial Department of Education (Grant No. Q200713001);Scientific Innovation Team Project of Hubei Provincial Department of Education (Grant No. T200809);supported by National Natural Science Foundation of China (Grant No. 10771032)

摘　　要：In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding steady-state problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some non-existence results for non-constant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding steady-state problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some non-existence results for non-constant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.

关 键 词：a diffusive predator-prey model steady states global stability a priori-estimates NON-EXISTENCE 

分 类 号：O175.2[理学—数学] Q141[理学—基础数学]