Dynamics of a Scalar Population Model with Delayed Allee Effect

被引：6

作者：

Chang, Xiaoyuan ^{[1
]}

Shi, Junping ^{[2
]}

Zhang, Jimin ^{[3
]}

机构：

[1] Harbin Univ Sci & Technol, Sch Sci, Harbin 150080, Heilongjiang, Peoples R China

[2] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

[3] Heilongjiang Univ, Sch Math Sci, Harbin 150080, Heilongjiang, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2018年 / 28卷 / 12期

关键词：

Allee effect; time delay; Hopf bifurcation; basin of attraction; bistability; BIFURCATION-ANALYSIS; BEHAVIOR;

D O I：

10.1142/S0218127418501535

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A scalar population model with delayed growth rate of Allee effect type is considered in this paper. The stability of equilibria and associated supercritical Hopf bifurcations are analyzed. The basins of attraction of the two locally stable equilibria are characterized in terms of parameter values. In particular, when the time delay is large, the basin of attraction of the persistence equilibrium and limit cycle shrinks to a single point, so a global extinction of population occurs as a combined result of Allee effect and time delay.

引用

页数：15

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