STABILITY AND BIFURCATION IN A LOGISTIC EQUATION WITH PIECEWISE CONSTANT ARGUMENTS

被引：3

作者：

Zhang, Chunrui ^{[2
]}

Zheng, Baodong ^{[1
]}

Zhang, Yazhuo ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[2] NE Forestry Univ, Dept Math, Harbin 150040, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2009年 / 19卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Logistic equation; piecewise constant arguments; stability; Hopf bifurcation; DIFFERENTIAL-EQUATIONS; GLOBAL STABILITY;

D O I：

10.1142/S0218127409023706

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A logistic equation with piecewise constant arguments is investigated. Firstly, the linear stability of the model is studied. It is found that there exists a Hopf bifurcation when the parameter passes a critical value. Then the explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solution is derived by using the normal form method and center manifold theorem. Finally, computer simulations are performed to illustrate the analytical results found.

引用

页码：1373 / 1379

页数：7

共 12 条

[1]

[Anonymous], 1991, DIFFERENTIALANDINTEG

[2]

Dai L., 2004, Communications in Nonlinear Science and Numerical Simulation, V9, P417, DOI 10.1016/S1007-5704(02)00137-5

[3] Asymptotic behaviour of solutions to abstract logistic equations [J].

Dyson, Janet ;

Villella-Bressan, Rosanna ;

Webb, Glenn F. .

MATHEMATICAL BIOSCIENCES, 2007, 206 (02) :216-232

[4] On quasi-periodic solutions of differential equations with piecewise constant argument [J].

Küpper, T ;

Yuan, R .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 267 (01) :173-193

[5] Global stability and chaos in a population model with piecewise constant arguments [J].

Liu, PZ ;

Gopalsamy, K .

APPLIED MATHEMATICS AND COMPUTATION, 1999, 101 (01) :63-88

[6] Persistence, contractivity and global stability in logistic equations with piecewise constant delays [J].

Muroya, Y .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 270 (02) :602-635

[7]

Muroya Y., 2003, HOKKAIDO MATH J, V32, P75

[8] On the global attractivity for a logistic equation with piecewise constant arguments [J].

Uesugi, K ;

Muroya, Y ;

Ishiwata, E .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 294 (02) :560-580

[9]

WANG C, 2002, J MATH ANAL APPL, V298, P298

[10] On the logistic delay differential equations with piecewise constant argument and quasi-periodic time dependence [J].

Yuan, R .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 274 (01) :124-133

← 1 2 →