| Local Lyapunov Exponents and characteristics of fixed／periodic points embedded within a chaotic attractor |
| |
| 作者姓名： | ALI M SAHA L.M |
| |
| 作者单位： | Department of Mathematics，Faculty of Mathematical Science，Delhi University，Department of Mathematics，Zakir Husain College，Delhi University Delhi 110007，India，New Delhi 110002，India |
| |
| 摘 要： | A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring trajectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1＞0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an altemative method to calculate λ1has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.
|
| 关 键 词： | 动力系统 Lyapunov指数 混乱系统 数学理论 |
| 收稿时间： | 12 August 2004 |
| 修稿时间： | 21 January 2005 |
Local lyapunov exponents and characteristics of fixed/periodic points embedded within a chaotic attractor |
| |
| ALI M,SAHA L.M.Local lyapunov exponents and characteristics of fixed/periodic points embedded within a chaotic attractor[J].Journal of Zhejiang University Science,2005,6(4):296-304. |
| |
| Authors: | M Ali L M Saha |
| |
| Institution: | (1) Department of Mathematics, Faculty of Mathematical Science, Delhi University, 10007 Delhi, India;(2) Department of Mathematics, Zakir Husain College, Delhi University, 110002 New Delhi, India |
| |
| Abstract: | A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring trajectories
over a chaotic attractor. Knowledge of the Largest Lyapunov Exponentλ
1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ
1 >0) or not (λ
1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent
where an alternative method to calculateλ
1 has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic
attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic
orbit within it. |
| |
| Keywords: | Chaotic attractor Largest Lyapunov Exponent Local Lyapunov Exponents |
| 本文献已被 CNKI 万方数据 SpringerLink 等数据库收录！ |
