THEORY OF ROTATED EQUATIONS AND APPLICATIONS TO A POPULATION MODEL

被引：42

作者：

Han, Maoan ^{[1
,2
]}

Hou, Xiaoyan ^{[1
]}

Sheng, Lijuan ^{[1
]}

Wang, Chaoyang ^{[3
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Peoples R China

[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Periodic solution; rotated equation; saddle-node bifurcation;

D O I：

10.3934/dcds.2018089

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a family of scalar periodic equations with a parameter and establish theory of rotated equations, studying the behavior of periodic solutions with the change of the parameter. It is shown that a stable (completely unstable) periodic solution of a rotated equation varies monotonically with respect to the parameter and a semi-stable periodic solution splits into two periodic solutions or disappears as the parameter changes in one direction or another. As an application of the obtained results, we give a further study of a piecewise smooth population model verifying the existence of saddle-node bifurcation.

引用

页码：2171 / 2185

页数：15

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