The predator-prey model with two limit cycles
type: Item
instance of: scholarly article
title: The predator-prey model with two limit cycles
zbMATH Open document ID: 0693.34034
DOI: 10.1007/BF02006184
author: Yongtai Ren
author: Li Han
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1989-01-01T00:00:00Z
review text: The paper investigates the predator-prey system: \[ \dot x=k_ 1(x-dx)- k(x)y,\quad \dot y=(-k_ 3+\beta k(x))y \] with \(k(x)=k_ 2(x)\), \(x\leq \tau\); \(k(x)=k_ 2\tau\), \(x>\tau\), where \(\alpha,\beta,\tau;\) \(k_ 1,k_ 2,k_ 3\) are positive constants. The main results are 1. The system has no limit cycle if \(k_ 3-\beta k_ 2\tau \geq 0\) 2. If \(k_ 3-\beta k_ 2\tau <0\), \(k_ 1+k_ 3-\beta k_ 2\tau >0\) and \(0<\alpha \ll 1\), the system has at least two limit cycles in the first quadrant, one of which is around the singular point (x,y), where \(x=k_ 3/\beta k_ 2\), \(y=(k_ 1-\alpha x)/k_ 2.\)
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 4134481
zbMATH Keywords: predator-prey system
zbMATH Keywords: limit cycle
Wikidata QID: Q115610214
reviewed by: Li-Ren Sheng
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4134481