An extension of Sharkovsky's theorem to periodic difference equations

被引：34
作者：
Alsharawi, Z
Angelos, J
Elaydi, S [1 ]
Rakesh, L
机构：
[1] Trinity Univ, San Antonio, TX 78212 USA
[2] Cent Michigan Univ, Mt Pleasant, MI 48858 USA
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2006年 / 316卷 / 01期
关键词：
periodic orbits; difference equations; geometric cycles; skew-product dynamical systems; nonautonomous;
D O I：
10.1016/j.jmaa.2005.04.059
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present an extension of Sharkovsky's theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：128 / 141
页数：14
相关论文
共 30 条
[1]  
BLOCK L, 1992, DYNAMICS 1 DIMENSION
[2]   PERIODIC-SOLUTIONS TO NONAUTONOMOUS DIFFERENCE-EQUATIONS [J].
CLARK, ME ;
GROSS, LJ .
MATHEMATICAL BIOSCIENCES, 1990, 102 (01) :105-119
[3]   NONAUTONOMOUS LOGISTIC EQUATIONS AS MODELS OF THE ADJUSTMENT OF POPULATIONS TO ENVIRONMENTAL-CHANGE [J].
COLEMAN, BD .
MATHEMATICAL BIOSCIENCES, 1979, 45 (3-4) :159-173
[4]   A periodically forced Beverton-Holt equation [J].
Cushing, JM ;
Henson, SM .
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2002, 8 (12) :1119-1120
[5]  
Cushing JM, 2001, J DIFFER EQU APPL, V7, P859
[6]  
Devaney RL., 1992, A first course in chaotic dynamical systems: Theory and Experiment
[7]   The necessary and sufficient conditions of existence of periodic solutions of nonautonomous difference equations [J].
El-Owaidy, H ;
Mohamed, HY .
APPLIED MATHEMATICS AND COMPUTATION, 2003, 136 (2-3) :345-351
[8]   Global stability of periodic orbits of non-autonomous difference equations and population biology [J].
Elaydi, S ;
Sacker, RJ .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 208 (01) :258-273
[9]   On a converse of Sharkovsky's Theorem [J].
Elaydi, S .
AMERICAN MATHEMATICAL MONTHLY, 1996, 103 (05) :386-392
[10]  
Elaydi S., 2005, An introduction to difference equations
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