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Dynamical Response of a Van der Pol System with an External Harmonic Excitation and Fractional Derivative

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Discontinuity and Complexity in Nonlinear Physical Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 6))

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Abstract

We examined the Van der Pol system with external forcing and a memory possessing fractional damping term. Calculating the basins of attraction we showed broad spectrum of nonlinear behaviour connected with sensitivity to the initial conditions. To quantify dynamical response of the system we propose the statistical 0–1 test. The results have been confirmed by bifurcation diagrams, phase portraits and Poincare sections.

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Acknowledgements

The authors gratefully acknowledge the support of the 7th Framework Programme FP7- REGPOT-2009-1, under Grant Agreement No. 245479. The authors are grateful prof. Stefano Lenci for discussions.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, PL-20-618, Lublin, Poland

    Arkadiusz Syta & Grzegorz Litak

Authors
  1. Arkadiusz Syta
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  2. Grzegorz Litak
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Correspondence to Arkadiusz Syta .

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Editors and Affiliations

  1. Department of Electrical Engineering, Polytechnic Institute of Porto Institute of Engineering, Porto, Portugal

    J. A. Tenreiro Machado

  2. Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. Department of Mechanical Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois, USA

    Albert C J Luo

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Syta, A., Litak, G. (2014). Dynamical Response of a Van der Pol System with an External Harmonic Excitation and Fractional Derivative. In: Machado, J., Baleanu, D., Luo, A. (eds) Discontinuity and Complexity in Nonlinear Physical Systems. Nonlinear Systems and Complexity, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-01411-1_6

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  • DOI: https://doi.org/10.1007/978-3-319-01411-1_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01410-4

  • Online ISBN: 978-3-319-01411-1

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