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Fractional Rayleigh–Duffing-like system and its synchronization

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Abstract

This paper presents a periodically driven Rayleigh–Duffing-like system with the function x|x|. It is proven via the Melnikov function method that the quadratic function x|x| induces Smale horseshoes to the Rayleigh–Duffing-like system. The Rayleigh–Duffing-like oscillator with fractional order is also discussed, and results of computer simulation demonstrate the chaotic dynamic behaviors of the system. Furthermore, two fractional Rayleigh–Duffing-like systems are synchronized by active control technology, the method based on state observer and nonlinear feedback method. Numerical results validate the effectiveness and applicability of the proposed synchronization schemes.

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Acknowledgements

This work was supported by grants from the National Natural Science Foundation of China (Nos. 71140004, 11171238, 10971186, 61170129).

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Authors and Affiliations

  1. Department of Computer Sciences and Engineering, Zhangzhou Normal University, Zhang’zhou, Fu’jian, 363000, P.R. China

    Yan-Lan Zhang

  2. College of Mathematics, Sichuan University, Cheng’du, Si’chuan, 610064, P.R. China

    Yan-Lan Zhang & Mao-Kang Luo

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  1. Yan-Lan Zhang
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  2. Mao-Kang Luo
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Correspondence to Mao-Kang Luo.

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Zhang, YL., Luo, MK. Fractional Rayleigh–Duffing-like system and its synchronization. Nonlinear Dyn 70, 1173–1183 (2012). https://doi.org/10.1007/s11071-012-0521-0

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  • DOI: https://doi.org/10.1007/s11071-012-0521-0

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