Passive control of chaotic system with multiple strange attractors |
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Authors: | Song Yun-Zhong Zhao Guang-Zhou and Qi Dong-Lian |
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Institution: | College of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China; College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China |
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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. |
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Keywords: | chaos passive control the
Newton--Leipnik equation attractor |
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