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A fractional order HP memristive system with a line of equilibria, its bifurcation analysis, circuit simulation and ARM-FPGA-based implementation

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Abstract

In this research work, we propose to investigate the effect of fractional-order on the dynamics of a four dimensional (4D) chaotic system by adding a new model of a memristor, which is an essential electronic element with interesting applications. First introduced by Li et al. (Int J Circuit Theory Appl 42(11):1172–1188, 2014, https://doi.org/10.1002/cta.1912), the original system is investigated prior to the more detailed study by Pham et al., The system is found to be self-excited, has a line of equilibrium which are all unstable with regards to the stability condition of fractional-order systems. The bifurcation tools associated with lyapunov exponents reveal the rich dynamics behavior of the proposed system. Our analysis shows that the degree of complexity of the system increases as the fractional-order decreases from 1 to 0.97. Of most/particuar interest, an analog electronic circuit is designed and implemented in PSPICE for verification and confirmed by laboratory experimental measurements. Finally, an ARM-FPGA-based implementation of the 4D fractional-order chaotic system is presented in this work to illustrate the performance of the proposed scheme.

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Authors and Affiliations

  1. Laboratory of Mechanics, Materials and Structures Faculty of Science, Department of Physics, University of Yaounde 1, P.O. Box 812, Yaounde, Cameroon

    Tantoh Bitomo Francis Richard & Siewe Siewe Martin

  2. Laboratory of Condense Matter, Electronics and Signal Processing Faculty of Science, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Kammogne Soup Tewa Alain

  3. Research and Development Centre, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai, Tamil Nadu, 600 062, India

    Sundarapandian Vaidyanathan

  4. Digital Systems Group - Department of Electronics, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), 72840, Tonantzintla, Puebla, Mexico

    Daniel Clemente-Lopez

  5. Faculty of Electronics Sciences, Benemérita Universidad Autónoma de Puebla, 72000, Puebla, Mexico

    Jesus M. Munoz-Pacheco

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  1. Tantoh Bitomo Francis Richard
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Richard, T.B.F., Alain, K.S.T., Vaidyanathan, S. et al. A fractional order HP memristive system with a line of equilibria, its bifurcation analysis, circuit simulation and ARM-FPGA-based implementation. Analog Integr Circ Sig Process 118, 91–107 (2024). https://doi.org/10.1007/s10470-023-02199-z

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