Bifurcation analysis and chaos in a discrete reduced Lorenz system

被引：60

作者：

Elabbasy, E. M. ^{[1
]}

Elsadany, A. A. ^{[2
]}

Zhang, Yue ^{[3
]}

机构：

[1] Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt

[2] Suez Canal Univ, Fac Comp & Informat, Dept Basic Sci, Ismailia 41522, Egypt

[3] Northeastern Univ, Inst Syst Sci, Shenyang 110004, Liaoning, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 228卷

关键词：

Discrete Lorenz system; Chaotic behavior; Neimark-Sacker bifurcation; Lyapunov exponents; HOPF-BIFURCATION; DYNAMICAL BEHAVIORS; MODEL;

D O I：

10.1016/j.amc.2013.11.088

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the discrete reduced Lorenz system is considered. The dynamical behavior of the system is investigated. The existence and stability of the fixed points of this system are derived. The conditions for existence of a pitchfork bifurcation, flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. The complex dynamics, bifurcations and chaos are displayed by numerical simulations. Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.

引用

页码：184 / 194

页数：11

共 25 条

[21] COMPUTATION OF STABILITY CONDITION FOR HOPF BIFURCATION OF DIFEOMORPHISMS ON R2 [J].

WAN, YH .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1978, 34 (01) :167-175

[22] Hopf bifurcation analysis in a delayed Nicholson blowflies equation [J].

Wei, JJ ;

Li, MY .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 60 (07) :1351-1367

[23]

Wiggins S., 2003, Texts in Applied Mathematics, V2, DOI DOI 10.1007/978-1-4757-4067-7

[24]

Xie V., 2007, J INF SECUR COMMUN, V6, P187

[25] Dynamical behaviors and chaos control in a discrete functional response model [J].

Zhang, Yue ;

Zhang, Qingfing ;

Zhao, Lichun ;

Yang, Chunyu .

CHAOS SOLITONS & FRACTALS, 2007, 34 (04) :1318-1327

← 1 2 3 →