Estimating the bound for the generalized Lorenz system

doi:10.1088/1674-1056/19/1/010505

中国物理B ›› 2010, Vol. 19 ›› Issue (1): 10505-010505.doi: 10.1088/1674-1056/19/1/010505

Estimating the bound for the generalized Lorenz system

郑宇, 张晓丹

Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China

收稿日期:2008-10-10 修回日期:2009-07-15 出版日期:2010-01-15 发布日期:2010-01-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 60674059), and Research Fund of University of Science and Technology Beijing, China (Grant No. 00009010).

Estimating the bound for the generalized Lorenz system

Zheng Yu(郑宇)^† and Zhang Xiao-Dan(张晓丹)

Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China

Received:2008-10-10 Revised:2009-07-15 Online:2010-01-15 Published:2010-01-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 60674059), and Research Fund of University of Science and Technology Beijing, China (Grant No. 00009010).

摘要/Abstract

摘要： A chaotic system is bounded, and its trajectory is confined to a certain region which is called the chaotic attractor. No matter how unstable the interior of the system is, the trajectory never exceeds the chaotic attractor. In the present paper, the sphere bound of the generalized Lorenz system is given, based on the Lyapunov function and the Lagrange multiplier method. Furthermore, we show the actual parameters and perform numerical simulations.

Abstract: A chaotic system is bounded, and its trajectory is confined to a certain region which is called the chaotic attractor. No matter how unstable the interior of the system is, the trajectory never exceeds the chaotic attractor. In the present paper, the sphere bound of the generalized Lorenz system is given, based on the Lyapunov function and the Lagrange multiplier method. Furthermore, we show the actual parameters and perform numerical simulations.

Key words: chaos, generalized Lorenz system, Lyapunov function, Lagrange multiplier method

中图分类号: (Numerical simulations of chaotic systems)

05.45.Pq

02.60.Lj (Ordinary and partial differential equations; boundary value problems) 05.45.Gg (Control of chaos, applications of chaos)

郑宇, 张晓丹. Estimating the bound for the generalized Lorenz system[J]. 中国物理B, 2010, 19(1): 10505-010505.

Zheng Yu(郑宇) and Zhang Xiao-Dan(张晓丹) . Estimating the bound for the generalized Lorenz system[J]. Chin. Phys. B, 2010, 19(1): 10505-010505.

参考文献 16

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Estimating the bound for the generalized Lorenz system

Estimating the bound for the generalized Lorenz system

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