Eur. Phys. J. Special Topics 228, 1969-1981 (2019)
https://doi.org/10.1140/epjst/e2019-800222-7

Regular Article

Antimonotonicity and multistability in a fractional order memristive chaotic oscillator

¹ School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, P.R. China
² Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA
³ Center for Nonlinear Dynamics, Defence University, Bishoftu, Ethiopia
⁴ Department of Computer Science and Engineering, University of Kurdistan-Hewler, Erbil, Iraq
⁵ Department of Biomedical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15875-4413, Iran
⁶ Department of information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah, Saudi Arabia
⁷ Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
⁸ NAAM Research Group, King Abdulaziz University, Jeddah, Saudi Arabia

^a e-mail: fahimenazarimehr@yahoo.com

Received: 9 December 2018
Received in final form: 5 February 2019
Published online: 14 October 2019

Abstract

A memristor diode bridge chaotic circuit is proposed in this paper. The proposed oscillator has only one nonlinear element in the form of memristor. Dynamical properties of the proposed oscillator are investigated. The fractional order model of the oscillator is designed using Grünwald–Letnikov (GL) method. Bifurcation diagrams are plotted which shows that the proposed oscillator exhibits multistability. Finally, the antimonotonicity property of the fractional order oscillator is discussed in detail with two control parameters. Such property has not been explored for fractional order systems before.