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

doi:10.1007/s10473-020-0517-7

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (5): 1459-1476.doi: 10.1007/s10473-020-0517-7

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

苏涛, 张国宝

Colloge of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

收稿日期:2018-10-29 修回日期:2020-02-24 出版日期:2020-10-25 发布日期:2020-11-04
通讯作者: Guobao ZHANG E-mail:zhanggb2011@nwnu.edu.cn
作者简介:Tao SU,E-mail:970913788@qq.com
基金资助:
This work was supported by NSF of China (11861056), Gansu Provincial Natural Science Foundation (18JR3RA093).

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

Tao SU, Guobao ZHANG

Colloge of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2018-10-29 Revised:2020-02-24 Online:2020-10-25 Published:2020-11-04
Contact: Guobao ZHANG E-mail:zhanggb2011@nwnu.edu.cn
Supported by:
This work was supported by NSF of China (11861056), Gansu Provincial Natural Science Foundation (18JR3RA093).

摘要/Abstract

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

关键词: predator-prey system, ratio-dependent functional response, discrete diffusion, invasion traveling waves

Abstract: 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

Key words: predator-prey system, ratio-dependent functional response, discrete diffusion, invasion traveling waves

中图分类号:

34A33

苏涛, 张国宝. INVASION TRAVELING WAVES FOR A DISCRETE DIFFUSIVE RATIO-DEPENDENT PREDATOR-PREY MODEL[J]. 数学物理学报(英文版), 2020, 40(5): 1459-1476.

Tao SU, Guobao ZHANG. INVASION TRAVELING WAVES FOR A DISCRETE DIFFUSIVE RATIO-DEPENDENT PREDATOR-PREY MODEL[J]. Acta mathematica scientia,Series B, 2020, 40(5): 1459-1476.

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

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

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