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Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors pp 181–202Cite as

Dynamic Analysis, Electronic Circuit Realization of Mathieu-Duffing Oscillator and Its Synchronization with Unknown Parameters and External Disturbances

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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 133))

Abstract

This chapter deals with dynamic analysis, electronic circuit realization and adaptive function projective synchronization (AFPS) of two identical coupled Mathieu-Duffing oscillators with unknown parameters and external disturbances. The dynamics of the Mathieu-Duffing oscillator is investigated with the help of some classical nonlinear analysis techniques such as bifurcation diagrams, Lyapunov exponent plots, phase portraits as well as frequency spectrum. It is found that the oscillator experiences very rich and striking behaviors including periodicity, quasi-periodicity and chaos. An appropriate electronic circuit capable to mimic the dynamics of the Mathieu-Duffing oscillator is designed. The correspondences are established between the parameters of the system model and electronic components of the proposed circuit. A good agreement is obtained between the experimental measurements and numerical results. Furthermore, based on Lyapunov stability theory, adaptive controllers and sufficient parameter updating laws are designed to achieve the function projective synchronization between two identical drive-response structures of Mathieu-Duffing oscillators. The external disturbances are taken into account in the drive and response systems in order to verify the robustness of the proposed strategy. Analytical calculations and numerical simulations are performed to show the effectiveness and feasibility of the method.

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Acknowledgements

V. Kamdoum Tamba wishes to thank Dr. Sifeu Takougang Kingni (University of Maroua, Cameroon) for interesting discussions and careful reading of the chapter.

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Authors and Affiliations

  1. Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, P. O. Box: 134, Bandjoun, Cameroon

    Victor Kamdoum Tamba & François Kapche Tagne

  2. Laboratory of Electronics and Signal Processing (LETS), Department of Physics, Faculty of Science, University of Dschang, P. O. Box: 67, Dschang, Cameroon

    Victor Kamdoum Tamba, Elie Bertrand Megam Ngouonkadi & Hilaire Bertrand Fotsin

Authors
  1. Victor Kamdoum Tamba
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  2. François Kapche Tagne
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  3. Elie Bertrand Megam Ngouonkadi
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  4. Hilaire Bertrand Fotsin
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Corresponding author

Correspondence to Victor Kamdoum Tamba .

Editor information

Editors and Affiliations

  1. School of Electronics and Telecommunications, Hanoi University of Science and Technology, Hanoi, Vietnam

    Viet-Thanh Pham

  2. Research and Development Centre, Vel Tech University, Chennai, Tamil Nadu, India

    Sundarapandian Vaidyanathan

  3. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Christos Volos

  4. Division of Dynamics, Faculty of Mechanical Engineering, Lodz University of Technology, Łódź, Poland

    Tomasz Kapitaniak

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Tamba, V.K., Tagne, F.K., Ngouonkadi, E.B.M., Fotsin, H.B. (2018). Dynamic Analysis, Electronic Circuit Realization of Mathieu-Duffing Oscillator and Its Synchronization with Unknown Parameters and External Disturbances. In: Pham, VT., Vaidyanathan, S., Volos, C., Kapitaniak, T. (eds) Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors. Studies in Systems, Decision and Control, vol 133. Springer, Cham. https://doi.org/10.1007/978-3-319-71243-7_8

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  • DOI: https://doi.org/10.1007/978-3-319-71243-7_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71242-0

  • Online ISBN: 978-3-319-71243-7

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