Active Realization of Fractional-Order Integrators and Their Application in Multiscroll Chaotic Systems
Jesus M. Munoz-Pacheco,
Luis Carlos Lujano-Hernández,
Carlos Muñiz-Montero,
Akif Akgül,
Luis A. Sánchez-Gaspariano,
Chun-Biao Li,
Mustafa Çaǧri Kutlu
Affiliations
Jesus M. Munoz-Pacheco
Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, Ciudad Universitaria, 18 Sur y Avenida San Claudio San Manuel, Puebla 72592, Mexico
Luis Carlos Lujano-Hernández
Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, Ciudad Universitaria, 18 Sur y Avenida San Claudio San Manuel, Puebla 72592, Mexico
Carlos Muñiz-Montero
Ingeniería en Electrónica y Telecomunicaciones, Universidad Politécnica de Puebla, Tercer Carril del Ejido Serrano, S/N, San Mateo Cuanalá, Juan C. Bonilla, Puebla 72640, Mexico
Akif Akgül
Department of Electrical and Electronics Engineering, Faculty of Technology, Sakarya University of Applied Sciences, Geyve 54187, Serdivan, Sakarya, Turkey
Luis A. Sánchez-Gaspariano
Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, Ciudad Universitaria, 18 Sur y Avenida San Claudio San Manuel, Puebla 72592, Mexico
Chun-Biao Li
Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science and Technology, Nanjing 210044, China
Mustafa Çaǧri Kutlu
Department of Electrical and Electronics Engineering, Faculty of Technology, Sakarya University of Applied Sciences, Geyve 54187, Serdivan, Sakarya, Turkey
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.
