TWO CODIMENSION-TWO BIFURCATIONS OF A SECOND-ORDER DIFFERENCE EQUATION FROM MACROECONOMICS

被引：6

作者：

Zhong, Jiyu ^{[1
]}

Deng, Shengfu ^{[1
]}

机构：

[1] Lingnan Normal Univ, Sch Math & Stat, Zhanjiang 524048, Guangdong, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2018年 / 23卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Generalized flip bifurcation; resonance; Neimark-Sacker bifurcation; Chenciner bifurcation; invariant circle; INVARIANT CURVES;

D O I：

10.3934/dcdsb.2018062

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we mainly investigate two codimension-two bifurcations of a second-order difference equation from macroeconomics. Applying the center manifold theorem and the normal form analysis, we firstly give the parameter conditions for the generalized flip bifurcation, and prove that the system does not produce a strong resonance. Then, we compute the normal forms to obtain the parameter conditions for the Neimark-Sacker bifurcation, from which we present the conditions for the Chenciner bifurcation. In order to verify the correctness of our results, we also numerically simulate a half stable invariant circle and two invariant circles, one stable and one unstable, arising from the Chenciner bifurcation.

引用

页码：1581 / 1600

页数：20

共 18 条

[1]

[Anonymous], 2012, Applications of centre manifold theory

[2]

[Anonymous], 1998, ELEMENTS APPL BIFURC, DOI DOI 10.1007/B98848

[3]

ARROWSMITH D. K., 1990, An Introduction to Dynamical Systems

[4]

Chow S.-N., 1994, NORMAL FORMS BIFURCA

[5] On the global attractivity and oscillations in a class of second-order difference equations from macroeconomics [J].

El-Morshedy, Hassan A. .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2011, 17 (11) :1643-1650

[6]

Elaydi S., 2005, INTRO DIFFERENCE EQU

[7]

GUCKENHEIMER J., 1983, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, V42

[8]

Iooss G., 1979, Mathematical Studies, V36

[9] Global stability and boundedness in xn+1=cxn+f(xn-xn-1) [J].

Kent, CM ;

Sedaghat, H .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2004, 10 (13-15) :1215-1227

[10] Bifurcations in a second-order difference equation from macroeconomics [J].

Li, Shuping ;

Zhang, Weinian .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2008, 14 (01) :91-104

← 1 2 →