文献类型：期刊文献

中文题名：An analytical method for studying double Hopf bifurcations induced by two delays in nonlinear differential systems

英文题名：An analytical method for studying double Hopf bifurcations induced by two delays in nonlinear differential systems

作者：Ge, JuHong[1];Xu, Jian[2]

第一作者：Ge, JuHong

通讯作者：Ge, JH[1]

机构：[1]Henan Univ Econ & Law, Dept Math & Informat Sci, Zhengzhou 450046, Henan, Peoples R China;[2]Tongji Univ, Shanghai Inst Intelligent Sci & Technol, Shanghai 200092, Peoples R China

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Henan Univ Econ & Law, Dept Math & Informat Sci, Zhengzhou 450046, Henan, Peoples R China.|[1048425]河南财经政法大学数学与信息科学学院;[10484]河南财经政法大学;

年份：2020

卷号：63

期号：4

起止页码：597-602

中文期刊名：中国科学：技术科学英文版

外文期刊名：SCIENCE CHINA-TECHNOLOGICAL SCIENCES

收录：;EI(收录号：20194407598553);Scopus(收录号：2-s2.0-85074033590);WOS:【SCI-EXPANDED(收录号:WOS:000492238600002)】；CSCD:【CSCD2019_2020】；

基金：This work was supported by the National Natural Science Foundation of China (Grant Nos. 11872175, 11572224, 61603125 and 21130010), Young talents Fund of Henan University of Economics and Law, National Key Project Cultivation Project of Henan University of Economics and Law, and Key Research Project of Higher Education Institutions of Henan Province (Grant No. 18A110003).

语种：英文

中文关键词：analytical;methods;multiple;delays;double;Hopf;bifurcation;the;coexistence;of;periodic;motion

外文关键词：analytical methods; multiple delays; double Hopf bifurcation; the coexistence of periodic motion

摘要：An analytical method is introduced to investigate double Hopf bifurcations induced by two delays qualitatively and quantitatively.As an illustrative example,the clear procedure is demonstrated to study delay-induced weak resonant double Hopf bifurcation in a nonlinear system with multiple delays.When two delays are close to double Hopf bifurcation point,all solutions derived from the bifurcation are classified qualitatively and expressed explicitly.Numerical simulations are a good agreement with our theoretical analysis,and also already work in references.The results show that our work in this paper proposes a simple and valid method for investigating delay-induced double Hopf bifurcations.The important feature of our work is that the explicit expression of periodic solutions is easy to be obtained by solving algebraic equations.
An analytical method is introduced to investigate double Hopf bifurcations induced by two delays qualitatively and quantitatively. As an illustrative example, the clear procedure is demonstrated to study delay-induced weak resonant double Hopf bifurcation in a nonlinear system with multiple delays. When two delays are close to double Hopf bifurcation point, all solutions derived from the bifurcation are classified qualitatively and expressed explicitly. Numerical simulations are a good agreement with our theoretical analysis, and also already work in references. The results show that our work in this paper proposes a simple and valid method for investigating delay-induced double Hopf bifurcations. The important feature of our work is that the explicit expression of periodic solutions is easy to be obtained by solving algebraic equations.