Eur. Phys. J. Special Topics 226, 3747–3773 (2017)
https://doi.org/10.1140/epjst/e2018-00063-9

Regular Article

Fractional-order systems with diverse dynamical behaviour and their switching-parameter hybrid-synchronisation

¹ Department of Electrical Engineering, Tezpur University, Tezpur 784028, Assam, India
² Department of Electrical Engineering, National Institute of Technology, Silchar 788010, Assam, India

^a e-mail: manashitaborah@gmail.com

Received: 29 July 2017
Received in final form: 31 January 2018
Published online: 25 July 2018

Abstract

The paper proposes a total of four fractional-order systems (FOSs) that display a variety of nonlinear dynamical behaviour, each having a speciality of its own. The first is a fractional-order (FO) model of a hypogenetic jerk system that has four equilibrium points and exhibits asymmetric coexisting attractors. The second is a FO hypogenetic jerk system devoid of any equilibrium and displays hidden attractors. The third is an FOS that has surfaces of equilibria, displays hidden attractors and has an effective fractional dimension n_f = 2.982. A system having surface equilibria with dimension less than three is not reported so far, to the best of the authors’ knowledge. The fourth is that of an FOS that exhibits FO Hopf bifurcation leading to hyperchaos. The existence of diverse nonlinear behaviours and their subtle characteristics are studied, all ranging from coexisting to hidden attractors, FO chaotic to FO hyperchaotic nature, encompassing quasiperiodic, periodic and stable dynamics. In addition to these, a switching-parameter cum hybrid-synchronisation scheme is designed. The idea is to carry out hybrid synchronisation in the newly proposed FOSs when an abrupt change of parameter takes place. The circuit implementation results comply with that of the theoretical and simulated results and thus validate the proposals made in this work.