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Analog circuit design and optimal synchronization of a modified Rayleigh system

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Abstract

This paper addresses the problem of optimization of the synchronization of a chaotic modified Rayleigh system. We first introduce a four-dimensional autonomous chaotic system which is obtained by the modification of a two-dimensional Rayleigh system. Some basic dynamical properties and behaviors of this system are investigated. An appropriate electronic circuit (analog simulator) is proposed for the investigation of the dynamical behavior of the proposed system. Correspondences are established between the coefficients of the system model and the components of the electronic circuit. Furthermore, we propose an optimal robust adaptive feedback which accomplishes the synchronization of two modified Rayleigh systems using the controllability functions method. The advantage of the proposed scheme is that it takes into account the energy wasted by feedback coupling and the closed loop performance on synchronization. Also, a finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master–slave controller system is also presented to show the feasibility of the proposed scheme.

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Acknowledgments

The authors would like to thank the Nuclear Instrumentation Unit of the Nuclear Technology Section, Institute of Geological and Mining Research, for providing electronic equipments and facilities that helped to achieve the experimental part of the work. We also thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improving the final version of the paper, as well as the editors for their generous comments and support during the review process. Patrick Louodop acknowledges the support by Grant Nr. 2014/13272-1 Sao Paulo Research Foundation (FAPESP), Brazil.

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Authors and Affiliations

  1. Laboratory of Electronics and Signals Processing, Department of Physics, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Michaux Kountchou, Patrick Louodop & Hilaire Fotsin

  2. Nuclear Technology Section, Institute of Geological and Mining Research, P.O. Box 4110, Yaoundé, Cameroon

    Michaux Kountchou &  Saïdou

  3. Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon

    Samuel Bowong

  4. UMI 209 IRD&UPMC UMMISCO, Bondy, France

    Samuel Bowong

  5. LIRIMA, Project Team GRIMCAPE, Yaoundé, Cameroon

    Samuel Bowong

  6. The African Center of Excellence in Information and Communication Technologies (CETIC), University of Yaounde 1, Yaoundé, Cameroon

    Samuel Bowong

  7. Nuclear Physics Laboratory, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon

    Saïdou

  8. Instituto de Física Teórica, UNESP, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, São Paulo, 01140-070, Brazil

    Patrick Louodop

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  1. Michaux Kountchou
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  2. Patrick Louodop
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  4. Hilaire Fotsin
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Correspondence to Michaux Kountchou.

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Kountchou, M., Louodop, P., Bowong, S. et al. Analog circuit design and optimal synchronization of a modified Rayleigh system. Nonlinear Dyn 85, 399–414 (2016). https://doi.org/10.1007/s11071-016-2694-4

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  • DOI: https://doi.org/10.1007/s11071-016-2694-4

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