PERSISTENCE AND THE GLOBAL DYNAMICS OF THE POSITIVE SOLUTIONS FOR A RATIODEPENDENT PREDATOR-PREY SYSTEM WITH A CROWDING TERM IN THE PREY EQUATION

doi:10.1016/S0252-9602(16)30032-7

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (3): 689-703.doi: 10.1016/S0252-9602(16)30032-7

PERSISTENCE AND THE GLOBAL DYNAMICS OF THE POSITIVE SOLUTIONS FOR A RATIODEPENDENT PREDATOR-PREY SYSTEM WITH A CROWDING TERM IN THE PREY EQUATION

曾宪忠¹, 顾永耕²

1. School of Mathematics and Computing Science, Hunan University of Science and Technology Xiangtan 411201, China;
2. Department of Mathematics, Hunan Normal University, Changsha 410081, China

收稿日期:2015-04-13 修回日期:2015-11-20 出版日期:2016-06-25 发布日期:2016-06-25
作者简介:Xianzhong ZENG,E-mail:zxzh217@sohu.com,xzzeng@hnust.edu.cn;Yonggeng GU,E-mail:gyg337@126.com
基金资助:
This work was supported by the National Natural Science Foundation of China (11271120, 11426099) and the Project of Hunan Natural Science Foundation of China (13JJ3085).

PERSISTENCE AND THE GLOBAL DYNAMICS OF THE POSITIVE SOLUTIONS FOR A RATIODEPENDENT PREDATOR-PREY SYSTEM WITH A CROWDING TERM IN THE PREY EQUATION

Xianzhong ZENG¹, Yonggeng GU²

1. School of Mathematics and Computing Science, Hunan University of Science and Technology Xiangtan 411201, China;
2. Department of Mathematics, Hunan Normal University, Changsha 410081, China

Received:2015-04-13 Revised:2015-11-20 Online:2016-06-25 Published:2016-06-25
Supported by:
This work was supported by the National Natural Science Foundation of China (11271120, 11426099) and the Project of Hunan Natural Science Foundation of China (13JJ3085).

摘要/Abstract

摘要：

This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coefficient of the functional response is less than the coefficient of the intrinsic growth rates of the prey species. We demonstrated some special dynamical behaviors of the positive solutions of this system which the persistence of the coexistence of two species can be obtained when the crowding region in the prey equation only is designed suitably. Furthermore, we can obtain that under some conditions, the unique positive steady state solution of the system is globally asymptotically stable.

关键词: ratio-dependent predator-prey system, crowding effect, persistence, global stability

Abstract:

Key words: ratio-dependent predator-prey system, crowding effect, persistence, global stability

中图分类号:

35J57

曾宪忠, 顾永耕. PERSISTENCE AND THE GLOBAL DYNAMICS OF THE POSITIVE SOLUTIONS FOR A RATIODEPENDENT PREDATOR-PREY SYSTEM WITH A CROWDING TERM IN THE PREY EQUATION[J]. 数学物理学报(英文版), 2016, 36(3): 689-703.

Xianzhong ZENG, Yonggeng GU. PERSISTENCE AND THE GLOBAL DYNAMICS OF THE POSITIVE SOLUTIONS FOR A RATIODEPENDENT PREDATOR-PREY SYSTEM WITH A CROWDING TERM IN THE PREY EQUATION[J]. Acta mathematica scientia,Series B, 2016, 36(3): 689-703.

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PERSISTENCE AND THE GLOBAL DYNAMICS OF THE POSITIVE SOLUTIONS FOR A RATIODEPENDENT PREDATOR-PREY SYSTEM WITH A CROWDING TERM IN THE PREY EQUATION

PERSISTENCE AND THE GLOBAL DYNAMICS OF THE POSITIVE SOLUTIONS FOR A RATIODEPENDENT PREDATOR-PREY SYSTEM WITH A CROWDING TERM IN THE PREY EQUATION

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