Bifurcation and chaotic behavior in the Euler method for a Kaplan-Yorke prototype delay model

被引：17
作者：
Peng, MS [1 ]
机构：
[1] No Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China
来源：
CHAOS SOLITONS & FRACTALS | 2004年 / 20卷 / 03期
关键词：
D O I：
10.1016/S0960-0779(03)00408-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A discrete model with a simple cubic nonlinearity term is treated in the study the rich dynamics of a prototype delayed dynamical system under Euler discretization. The effect of breaking the symmetry of the system is to create a wide complex operating conditions which would not otherwise be seen. These include multiple steady states, complex periodic oscillations, chaos by period doubling bifurcations. (C) 2003 Elsevier Ltd. All rights reserved.
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页码：489 / 496
页数：8
相关论文
共 13 条
[1]   THE STABILITY OF SPECIAL SYMMETRIC-SOLUTIONS OF X(T) = ALPHA-F(X(T-1)) WITH SMALL AMPLITUDES [J].
DORMAYER, P .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 14 (08) :701-715
[2]  
DORMAYER P, 1989, J DIFF EQS, V122, P109
[3]  
HALE JK, 1977, THEORY FUNCTIONAL DI
[4]  
Iooss G., 1979, Bifurcation of Maps and Applications
[5]   ORDINARY DIFFERENTIAL EQUATIONS WHICH YIELD PERIODIC-SOLUTIONS OF DIFFERENTIAL DELAY EQUATIONS [J].
KAPLAN, JL ;
YORKE, JA .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1974, 48 (02) :317-324
[6]  
KAYMAKCALAN B, 1996, DYNAMICAL SYSTEMS ME
[7]   THE ASYMPTOTIC STABILITY OF X(N+1)-AX(N)+BX(N-K)=0 [J].
KURUKLIS, SA .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1994, 188 (03) :719-731
[8]   NOTE ON DIFFERENCE-DELAY EQUATIONS [J].
LEVIN, SA ;
MAY, RM .
THEORETICAL POPULATION BIOLOGY, 1976, 9 (02) :178-187
[9]   UNIQUENESS AND NONUNIQUENESS FOR PERIODIC-SOLUTIONS OF X'(T)=-G(X(T-1)) [J].
NUSSBAUM, RD .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1979, 34 (01) :25-54
[10]  
PENG M, IN PRESS BIFURCATION
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