Eur. Phys. J. Special Topics 228, 2035-2051 (2019)
https://doi.org/10.1140/epjst/e2019-900001-8

Regular Article

Coexistence of attractors in a simple chaotic oscillator with fractional-order-memristor component: analysis, FPGA implementation, chaos control and synchronization

¹ Centre for Non-Linear Dynamics, Defence University, Bishoftu, Ethiopia
² Institute of Energy, Mekelle University, Mek’ele, Ethiopia
³ Department of Mechanical, Petroleum and Gas Engineering, Faculty of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon
⁴ Ministry of Higher Education and Scientific Research, Baghdad, Iraq
⁵ Faculty of Computer Science and Engineering, Shahid Beheshti University, Velenjak, 19839-69411 Tehran, Iran
⁶ Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran

^a e-mail: fahimenazarimehr@yahoo.com

Received: 2 January 2019
Received in final form: 26 March 2019
Published online: 14 October 2019

Abstract

In this paper, the simplest chaotic oscillator with fractional-order-memristor component (SCOF) is proposed. Dynamical characteristics of the proposed chaotic oscillator are investigated both analytically and numerically. The results indicate that the proposed chaotic oscillator possesses novel dynamical characteristics: double-scroll chaotic attractor, four-scroll chaotic attractor and coexisting attractors. The proposed SCOF system is implemented in field programmable gate arrays (FPGA) using the Adomian decomposition method to verify the numerical simulation results. Finally, control and synchronization of the simple chaotic oscillator with fractional-order-memristor component is studied using the linear feedback control and the unidirectional linear error feedback coupling scheme, respectively.