A YING-YANG THEORY IN NONLINEAR DISCRETE DYNAMICAL SYSTEMS

被引：3
|
作者：
Luo, Albert C. J. [1 ]
机构：
[1] So Illinois Univ, Dept Mech & Ind Engn, Edwardsville, IL 62026 USA
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2010年 / 20卷 / 04期
关键词：
Ying-Yang; hidden dynamics; positive iterations; negative iterations; unstable period-doubling bifurcation; unstable saddle-node bifurcation; CHAOTIC BEHAVIOR; HENON; UNIVERSALITY; BIFURCATIONS; INSTABILITY; PARTICLES; MODELS; MAPS;
D O I：
10.1142/S0218127410026332
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper presents a Ying-Yang theory for nonlinear discrete dynamical systems considering both positive and negative iterations of discrete iterative maps. In the existing analysis, the solutions relative to "Yang" in nonlinear dynamical systems are extensively investigated. However, the solutions pertaining to "Ying" in nonlinear dynamical systems are investigated. A set of concepts on "Ying" and "Yang" in discrete dynamical systems are introduced to help one understand the hidden dynamics in nonlinear discrete dynamical systems. Based on the Ying-Yang theory, the periodic and chaotic solutions in nonlinear discrete dynamical system are discussed, and all possible, stable and unstable periodic solutions can be analytically predicted. A discrete dynamical system with the Henon map is investigated, as an example.
引用
收藏
页码：1085 / 1098
页数：14
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