Existence and the dynamical behaviors of the positive solutions for a ratio-dependent predator-prey system with the crowing term and the weak growth
type: Item
instance of: scholarly article
title: Existence and the dynamical behaviors of the positive solutions for a ratio-dependent predator-prey system with the crowing term and the weak growth
zbMATH Open document ID: 1401.35193
published in: Journal of Differential Equations
publication date: 2018-01-11T00:00:00Z
review text: The authors study a ratio-dependent predator-prey system with the crowding term and the weak growth in the prey equation. They obtain existence of multiple positive steady state solutions of the predator-prey system, and the dynamical behavior of its positive solutions. These results show that the predator and the prey possess not only the common coexistence, but also the very weak coexistence state in which both of the predator and the prey are very low. They may be used to explain some special phenomena which under some bad environment, the predator and the prey may still coexist.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 6824722
zbMATH Keywords: predator-prey system
zbMATH Keywords: crowding effect
zbMATH Keywords: multiple positive solutions
zbMATH Keywords: persistence
zbMATH Keywords: stability
author: Xianzhong Zeng
author: Yong-geng Gu
MaRDI profile type: Publication
full work available at URL: j.jde.2017.11.026
OpenAlex ID: W2772470027
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Existence and the dynamical behaviors of the positive solutions for a ratio-dependent predator-prey system with the crowing term and the weak growth (cites work)
cites work: Persistence and the global dynamics of the positive solutions for a ratio dependent predator-prey system with a crowding term in the prey equation

Existence and the dynamical behaviors of the positive solutions for a ratio-dependent predator-prey system with the crowing term and the weak growth (DOI)
DOI: 10.1016/J.JDE.2017.11.026

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