The Neimark-Sacker bifurcation of xn+1=δxn-2+xn-3/A+xn-3

Rongyan Zhang; Xiaohua Ding

doi:10.1080/10236190802357669

The Neimark-Sacker bifurcation of x_n+1=δx_n-2+x_n-3/A+x_n-3

Rongyan Zhang
, Xiaohua Ding^*

^*Corresponding author for this work

Harbin Institute of Technology Weihai

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this article, we investigate the existence and direction of the Neimark-Sacker bifurcation of the equation in the title with positive parameters and with arbitrary non-negative conditions. First, we study the existence of the Neimark-Sacker bifurcation of the system by analyzing the characteristic equation. Secondly, we investigate the direction and stability of the bifurcating invariant curve by using the normal form theory. Finally, computer simulation is performed to illustrate the analytical results found.

Original language	English
Pages (from-to)	775-784
Number of pages	10
Journal	Journal of Difference Equations and Applications
Volume	15
Issue number	8-9
DOIs	https://doi.org/10.1080/10236190802357669
State	Published - 2009
Externally published	Yes

Keywords

Difference equation
Neimark-Sacker bifurcation
Normal form
Stability

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10.1080/10236190802357669

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title = "The Neimark-Sacker bifurcation of xn+1=δxn-2+xn-3/A+xn-3",

abstract = "In this article, we investigate the existence and direction of the Neimark-Sacker bifurcation of the equation in the title with positive parameters and with arbitrary non-negative conditions. First, we study the existence of the Neimark-Sacker bifurcation of the system by analyzing the characteristic equation. Secondly, we investigate the direction and stability of the bifurcating invariant curve by using the normal form theory. Finally, computer simulation is performed to illustrate the analytical results found.",

keywords = "Difference equation, Neimark-Sacker bifurcation, Normal form, Stability",

author = "Rongyan Zhang and Xiaohua Ding",

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AU - Zhang, Rongyan

AU - Ding, Xiaohua

PY - 2009

Y1 - 2009

N2 - In this article, we investigate the existence and direction of the Neimark-Sacker bifurcation of the equation in the title with positive parameters and with arbitrary non-negative conditions. First, we study the existence of the Neimark-Sacker bifurcation of the system by analyzing the characteristic equation. Secondly, we investigate the direction and stability of the bifurcating invariant curve by using the normal form theory. Finally, computer simulation is performed to illustrate the analytical results found.

AB - In this article, we investigate the existence and direction of the Neimark-Sacker bifurcation of the equation in the title with positive parameters and with arbitrary non-negative conditions. First, we study the existence of the Neimark-Sacker bifurcation of the system by analyzing the characteristic equation. Secondly, we investigate the direction and stability of the bifurcating invariant curve by using the normal form theory. Finally, computer simulation is performed to illustrate the analytical results found.

KW - Difference equation

KW - Neimark-Sacker bifurcation

KW - Normal form

KW - Stability

UR - https://www.scopus.com/pages/publications/70549097340

U2 - 10.1080/10236190802357669

DO - 10.1080/10236190802357669

M3 - 文章

AN - SCOPUS:70549097340

SN - 1023-6198

VL - 15

SP - 775

EP - 784

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

IS - 8-9

ER -

The Neimark-Sacker bifurcation of x_n+1=δx_n-2+x_n-3/A+x_n-3

Abstract

Keywords

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