Passive control of chaotic system with multiple strange attractors
Song Yun-Zhong(宋运忠)a)b)†, Zhao Guang-Zhou(赵光宙)b), and Qi Dong-Lian(齐冬莲)b)
a College of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China; b College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
Abstract In this paper we present a new simple controller for a chaotic system, that is, the Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form. Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one, and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.
Received: 13 April 2005
Revised: 07 June 2006
Accepted manuscript online:
PACS:
05.45.Gg
(Control of chaos, applications of chaos)
Fund: Project supported by the
National Natural Science Foundation of China (Grant No 60374013), the
Natural Science Foundation
of Zhejiang Province (Grant Nos M603217 and
Y104414).
Cite this article:
Song Yun-Zhong(宋运忠), Zhao Guang-Zhou(赵光宙), and Qi Dong-Lian(齐冬莲) Passive control of chaotic system with multiple strange attractors 2006 Chinese Physics 15 2266
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
