POSITIVE STEADY STATES AND DYNAMICS FOR A DIFFUSIVE PREDATOR-PREY SYSTEM WITH A DEGENERACY  

作　　者：杨璐 张贻民 

机构地区：[1]School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China [2]Key Laboratory of Applied Mathematics and Complex Systems, Gansu 730000, China [3]Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China

出　　处：《Acta Mathematica Scientia》2016年第2期537-548,共12页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(11361053,11201204,11471148,11471330,145RJZA112)

摘　　要：In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by the degeneracy of the intra-specific pressures for the prey. By the bifurcation method, the degree theory, and a priori estimates, we discuss the existence and multiplicity of positive steady states. Moreover, by the comparison argument, we also discuss the dynamical behavior for the diffusive predator-prey system.In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by the degeneracy of the intra-specific pressures for the prey. By the bifurcation method, the degree theory, and a priori estimates, we discuss the existence and multiplicity of positive steady states. Moreover, by the comparison argument, we also discuss the dynamical behavior for the diffusive predator-prey system.

关 键 词：Predator-prey system steady state solution dynamical behavior 

分 类 号：O175[理学—数学]