Modelling, analysis and simulations of some chaotic systems using derivative with Mittag-Leffler kernel

Abstract

In this paper, a range of chaotic systems with some interesting behaviors such as multi-scroll attractors, self-excited and hidden attractors, period-doubling to chaos, periodic and chaotic bursting oscillations, and different multiple coexisting attractors have been considered and modelled with the new Atangana-Baleanu fractional derivative operator in time. Existence and uniqueness of general system as well as local stability analysis are examined. In the simulation framework, a range of chaotic patterns examined through time series were obtained for different instances of fractional orders. Comparison between the integer (with p = 1) and noninteger (0 < p < 1) order results are given. (C) 2019 Elsevier Ltd. All rights reserved.