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Volterra Series Approximation of a Class of Nonlinear Dynamical Systems Using the Adomian Decomposition Method

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Abstract

The relationship between the Adomian decomposition and the Volterra series is investigated and it is shown that the Volterra series can be considered as a specialization of the Adomian decomposition. Based on the relationship, the Volterra series can be calculated using an Adomian decomposition method whenever a convergent Volterra series representation exists. A class of nonlinear dynamical systems is considered and a new algorithm is introduced to compute the Volterra series representation for this class of nonlinear systems. The new method significantly simplifies the computation of the Volterra kernels and provides a new choice for the study of Volterra series of nonlinear dynamical systems.

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Acknowledgements

The authors gratefully acknowledge support from the UK Engineering and Physical Sciences Research Council (EPSRC) and the European Research Council (ERC). The authors also thank the reviewers for the helpful comments.

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Authors and Affiliations

  1. Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK

    Yuzhu Guo, L. Z. Guo, S. A. Billings, Daniel Coca & Z. Q. Lang

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  1. Yuzhu Guo
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  2. L. Z. Guo
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  3. S. A. Billings
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  4. Daniel Coca
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  5. Z. Q. Lang
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Correspondence to Yuzhu Guo.

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Guo, Y., Guo, L.Z., Billings, S.A. et al. Volterra Series Approximation of a Class of Nonlinear Dynamical Systems Using the Adomian Decomposition Method. Nonlinear Dyn 74, 359–371 (2013). https://doi.org/10.1007/s11071-013-0975-8

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