Eur. Phys. J. Special Topics 226, 3775–3789 (2017)
https://doi.org/10.1140/epjst/e2018-00012-8

Regular Article

Design of fractional-order hyper-chaotic multi-scroll systems based on hysteresis series

¹ School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, P.R. China
² Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, R. Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
³ UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
⁴ School of Mathematics, Anhui University, Hefei 230039, P.R. China

^a e-mail: lip_chenhut@126.com

Received: 25 April 2017
Received in final form: 29 September 2017
Published online: 25 July 2018

Abstract

This paper develops a novel fractional-order (FO) hyper-chaotic multi-scroll (FOHMS) system derived from a 4-dimensional FO linear system. Hysteresis function series are employed and added to the original system to extend the number of equilibrium points with index 2. The hyper-chaotic dynamics of the new FOHMS system is explored through phase portraits, largest Lyapunov exponents and Poincaré maps. A circuit for the 0.96-order FOHMS is implemented and several FOHMS attractors are observed. Numerical and circuit-based simulations show the feasibility of the theoretical formulation.