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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Chaos and Its Control in a Fractional Order Glucose-insulin Regulatory System

Journal of Applied Nonlinear Dynamics 11(4) (2022) 875--893 | DOI:10.5890/JAND.2022.12.008

P. Y. Dousseh$^{1}$, L. A. Hinvi$^{1,2}$, C.H. Miwadinou$^{1,3,4}$, A. V. Monwanou$^1$, J. B. Chabi Orou$^1$

$^1$ Laboratoire de M'ecanique des Fluides, de la Dynamique Nonlin'eaire et de la Mod'elisation des Syst`emes ; Institut de Math'ematiques et de Sciences Physiques, Porto-Novo, B'enin

$^2$ D'epartement des Sciences Industrielles et Techniques, INSTI-Lokossa, Universit'e Nationale des Sciences, Technologiques, Ing'enierie et Math'ematiques (UNSTIM) Abomey, B'enin

$^3$ D'epartement de Physique, ENS-Natitingou, Universit'e Nationale des Sciences, Technologies, Ing'enierie et Math'ematiques (UNSTIM) Abomey, B'enin

$^4$ Laboratoire de Physique et Applications de Natitingou, Universit'e Nationale des Sciences, Technologies, Ing'enierie et Math'ematiques (UNSTIM) Abomey, B'enin

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Abstract

In this paper, dynamic behaviors and chaos control of a Fractional Order Glucose-Insulin Regulatory System (FOGIRS) recently introduced in the literature are studied. Some interesting behaviors such as periodic motions, antimonotonicity, and period-doubling route to chaos are observed. Besides, it is found that the minimum effective dimension for the system to generate chaos is 2.904 in the conmensurate order case and 2.882 in the incommensurate order case. To control chaos in this system, two controllers are designed. First, a feedback controller to stabilize the chaotic system to one of its equilibrium points, and a robust adaptive fractional order sliding mode controller is used to globally stabilize the chaotic FOGIRS with uncertain dynamics. Numerical simulations are used to show the effectiveness of those controllers.

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