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Chaos control of a φ 6-Van der Pol oscillator driven by external excitation

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Abstract

This paper studies the dynamics of a φ 6-Van der Pol oscillator subjected to an external excitation. Numerical analysis is presented to observe its periodic and chaotic motions, and a method called Multiple-prediction Delayed Feedback Control is proposed to control chaos effectively via periodic feedback gain. The controller is designed based on plural Poincaré maps which are defined to regard the nonautonomous system as a T-periodic discrete time system, therefore, the stability of the closed-loop system can be evaluated from the theory of monodromy matrix. Numerical simulations are provided to illustrate the validity of the proposed control strategy.

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Authors and Affiliations

  1. Tokyo Institute of Technology, Tokyo, Japan

    Dasheng Liu

  2. Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1-I3-10, Ookayama, Meguro-ku, Tokyo, 152-8552, Japan

    Hiroshi Yamaura

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  1. Dasheng Liu
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  2. Hiroshi Yamaura
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Correspondence to Dasheng Liu.

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Liu, D., Yamaura, H. Chaos control of a φ 6-Van der Pol oscillator driven by external excitation. Nonlinear Dyn 68, 95–105 (2012). https://doi.org/10.1007/s11071-011-0206-0

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  • DOI: https://doi.org/10.1007/s11071-011-0206-0

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