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

被引：10

作者：

Ge, JuHong ^{[1
]}

Xu, Jian ^{[2
]}

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

来源：

SCIENCE CHINA-TECHNOLOGICAL SCIENCES | 2020年 / 63卷 / 04期

基金：

中国国家自然科学基金;

关键词：

analytical methods; multiple delays; double Hopf bifurcation; the coexistence of periodic motion; MULTISTABILITY COEXISTENCE; EFFICIENT METHOD; NEURAL-NETWORK; STABILITY; MODEL;

D O I：

10.1007/s11431-019-9673-6

中图分类号：

T [工业技术];

学科分类号：

08 ;

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.

引用

页码：597 / 602

页数：6

共 27 条

[1] SPATIOTEMPORAL ATTRACTORS GENERATED BY THE TURING-HOPF BIFURCATION IN A TIME-DELAYED REACTION-DIFFUSION SYSTEM [J].

An, Qi ;

Jiang, Weihua .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (02) :487-510

[2] Stability and Hopf bifurcation of controlled complex networks model with two delays [J].

Cao, Jinde ;

Guerrini, Luca ;

Cheng, Zunshui .

APPLIED MATHEMATICS AND COMPUTATION, 2019, 343 :21-29

[3] Bifurcations in an Internet congestion control system with distributed delay [J].

Cao, Yang .

APPLIED MATHEMATICS AND COMPUTATION, 2019, 347 :54-63

[4] A mathematical model of multiple delayed feedback control system of the gut microbiota-Antibiotics injection controlled by measured metagenomic data [J].

Dong, Yueping ;

Takeuchi, Yasuhiro ;

Nakaoka, Shinji .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2018, 43 :1-17

[5] Two delays induce Hopf bifurcation and double Hopf bifurcation in a diffusive Leslie-Gower predator-prey system [J].

Du, Yanfei ;

Niu, Ben ;

Wei, Junjie .

CHAOS, 2019, 29 (01)

[6] Effects of small delays on stability of singularly perturbed systems [J].

Fridman, E .

AUTOMATICA, 2002, 38 (05) :897-902

[7] Stability and Hopf bifurcation on four-neuron neural networks with inertia and multiple delays [J].

Ge, Juhong ;

Xu, Jian .

NEUROCOMPUTING, 2018, 287 :34-44

[8] Zero-Hopf bifurcation and multistability coexistence on a four-neuron network model with multiple delays [J].

Ge, Juhong ;

Xu, Jian ;

Li, ZhiQiang .

NONLINEAR DYNAMICS, 2017, 87 (04) :2357-2366

[9] Stability switches and bifurcation analysis in a coupled neural system with multiple delays [J].

Ge JuHong ;

Xu Jian .

SCIENCE CHINA-TECHNOLOGICAL SCIENCES, 2016, 59 (06) :920-931

[10] WEAK RESONANT DOUBLE HOPF BIFURCATIONS IN AN INERTIAL FOUR-NEURON MODEL WITH TIME DELAY [J].

Ge, Juhong ;

Xu, Jian .

INTERNATIONAL JOURNAL OF NEURAL SYSTEMS, 2012, 22 (01) :63-75

← 1 2 3 →