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Active Realization of Fractional-Order Integrators and Their Application in Multiscroll Chaotic Systems

Author

Listed:
  • Jesus M. Munoz-Pacheco
  • Luis Carlos Lujano-Hernández
  • Carlos Muñiz-Montero
  • Akif Akgül
  • Luis A. Sánchez-Gaspariano
  • Chun-Biao Li
  • Mustafa Çaǧri Kutlu
  • Carlos Aguilar-Ibanez

Abstract

This paper presents the design, simulation, and experimental verification of the fractional-order multiscroll Lü chaotic system. We base them on op-amp-based approximations of fractional-order integrators and saturated series of nonlinear functions. The integrators are first-order active realizations tuned to reduce the inaccuracy of the frequency response. By an exponential curve fitting, we got a convenient design equation for realizing fractional-order integrators of orders from 0.1 to 0.95. The results include simulations in SPICE of the mathematical description and the electronic implementation and experimental measurements that confirm them. Monte Carlo and sensitivity tests revealed a robust realization. Contrary to its passive counterparts, the suggested realizations significantly reduce design and implementation efforts by favoring resistors and capacitors with commercial values and reducing hardware requirements.

Suggested Citation

  • Jesus M. Munoz-Pacheco & Luis Carlos Lujano-Hernández & Carlos Muñiz-Montero & Akif Akgül & Luis A. Sánchez-Gaspariano & Chun-Biao Li & Mustafa Çaǧri Kutlu & Carlos Aguilar-Ibanez, 2021. "Active Realization of Fractional-Order Integrators and Their Application in Multiscroll Chaotic Systems," Complexity, Hindawi, vol. 2021, pages 1-16, January.
    • Handle: RePEc:hin:complx:6623855
    DOI: 10.1155/2021/6623855
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    Cited by:

    1. Echenausía-Monroy, J.L. & Gilardi-Velázquez, H.E. & Wang, Ning & Jaimes-Reátegui, R. & García-López, J.H. & Huerta-Cuellar, G., 2022. "Multistability route in a PWL multi-scroll system through fractional-order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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