Existence, uniqueness and stability of positive steady states to a prey-predator diffusion system  

作　　者：WANG MingXin WANG XuBo 

机构地区：[1]Science Research Center,Harbin Institute of Technology,Harbin 150080,China [2]Department of Mathematics,Southeast University,Nanjing 210018,China [3]Division of Natural Science and Mathematics,Macon State College,Macon,GA 31206,USA

出　　处：《Science China Mathematics》2009年第5期1031-1041,共11页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 10471022, 10771032);Natural Science Foundation of Jiangsu Province (Grant No. BK2006088)

摘　　要：In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semitrivial solution to the unique positive solution of the limiting system.In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semi-trivial solution to the unique positive solution of the limiting system.

关 键 词：prey-predator model positive solutions bifurcation existence and uniqueness STABILITY 35J55 35B25 92B05 

分 类 号：O175[理学—数学]