Eur. Phys. J. Special Topics 227, 837–850 (2018)
https://doi.org/10.1140/epjst/e2018-700137-2

Regular Article

Multistability and coexisting attractors in a fractional order Coronary artery system

¹ Center for Nonlinear Dynamics, Defence University, Bishoftu, Ethiopia
² Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
³ Department of Information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah, Saudi Arabia
⁴ Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia

^a e-mail: phamvietthanh@tdt.edu.vn

Received: 19 December 2017
Received in final form: 25 January 2018
Published online: 19 October 2018

Abstract

The present study investigates the dynamical properties of a fractional order coronary artery system and its control with uncertainties in the parameters. The fractional order model of the coronary artery system (FOCA) is derived using the Grünwald–Letnikov method and the properties of the FOCA system are discussed. Bifurcation plots of the system in the parameter space are derived and presented. The novelty of the paper is the identification of the multistable feature shown by the FOCA system, which has not been discussed in the research literature. Various coexisting attractors are also presented to show the multistability. An adaptive sliding mode controller is designed to stabilize the chaotic oscillations in the FOCA system. Numerical simulations are conducted to indicate the effectiveness of the controller.