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Asymptotic Solutions and Circuit Implementations of a Rayleigh Oscillator Including Cubic Fractional Damping Terms

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Abstract

This paper proposes a fractional-order Rayleigh oscillator model, which involves a cubic damping term described by fractional derivatives. The presence of such fractional damping term makes the analysis more difficult. A two-scale expansion method is employed for asymptotic solutions of the fractional-order Rayleigh oscillator. Then, an example is provided to compare the asymptotic solutions with the numerical solutions. The numerical results demonstrate the validity and applicability of the proposed method to solve fractional differential equations with high order fractional terms. Furthermore, an electronic circuit is designed to realize the fractional-order Rayleigh oscillator.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 61573194, Grant 61203232, Grant 61374180 and Grant 615573096, in part by the China Post-Doctoral Science Foundation under Grant 2013M530229, in part by the China Post-Doctoral Science Special Foundation under Grant 2014T70463, in part by the ‘Six Talent Peaks’ High Level Project of Jiangsu Province, China, under Grant ZNDW-004, in part by the Science Foundation of Nanjing University of Posts and Telecommunications under Grant NY213095 and in part by the 1311 Talents Project through the Nanjing University of Posts and Telecommunications.

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Authors and Affiliations

  1. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Min Xiao & Guoping Jiang

  2. Research Center for Complex Systems and Network Sciences, and Department of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

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  1. Min Xiao
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  2. Guoping Jiang
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Correspondence to Min Xiao.

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Xiao, M., Jiang, G. & Cao, J. Asymptotic Solutions and Circuit Implementations of a Rayleigh Oscillator Including Cubic Fractional Damping Terms. Circuits Syst Signal Process 35, 2041–2053 (2016). https://doi.org/10.1007/s00034-016-0268-9

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