INVASION TRAVELING WAVES FOR A DISCRETE DIFFUSIVE RATIO-DEPENDENT PREDATOR-PREY MODEL  

作　　者：Tao SU Guobao ZHANG 苏涛;张国宝(Colloge of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]Colloge of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China

出　　处：《Acta Mathematica Scientia》2020年第5期1459-1476,共18页数学物理学报（B辑英文版）

基　　金：supported by NSF of China(11861056);Gansu Provincial Natural Science Foundation(18JR3RA093).

摘　　要：This article is concerned with the existence of traveling wave solutions for a discrete diffusive ratio-dependent predator-prey model. By applying Schauder’s fixed point theorem with the help of suitable upper and lower solutions, we prove that there exists a positive constant c* such that when c > c* , the discrete diffusive predator-prey system admits an invasion traveling wave. The existence of an invasion traveling wave with c = c* is also established by a limiting argument and a delicate analysis of the boundary conditions.Finally, by the asymptotic spreading theory and the comparison principle, the non-existence of invasion traveling waves with speed c < c* is also proved.

关 键 词：predator-prey system ratio-dependent functional response discrete diffusion invasion traveling waves 

分 类 号：O175[理学—数学]