Eur. Phys. J. Special Topics 229, 1211-1230 (2020)
https://doi.org/10.1140/epjst/e2020-900169-1

Regular Article

Analysis and electronic circuit implementation of an integer- and fractional-order four-dimensional chaotic system with offset boosting and hidden attractors

¹ Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
² Research Unit of Automation and Applied Computer, Department of Electrical Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
³ Research Unit of Condensed Matter, Electronics and Signal Processing, Department of Physics, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon
⁴ Department of Mechanical, Petroleum and Gas Engineering, Faculty of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon

^a e-mail: koguiho2012@gmail.com

Received: 15 August 2019
Received in final form: 23 September 2019
Published online: 26 March 2020

Abstract

In this paper, an integer- and fractional-order form of a four-dimensional (4-D) chaotic system with hidden attractors is investigated using theoretical/numerical and analogue methods. The system is constructed not through the extension of a three-dimensional existing nonlinear system as in current approaches, but by modifying the well-known two-dimensional Lotka-Volterra system. The equilibrium point of the integer-order system is determined and its stability analysis is studied using Routh-Hurwitz criterion. When the selected bifurcation parameter is varied, the system exhibits various dynamical behaviors and features including intermittency route to chaos, chaotic bursting oscillations and offset boosting. Moreover, the fractional-order form of the system is examined through bifurcation analysis. It is revealed that chaotic behaviors still exist in the system with order less than four. To validate the numerical approaches, a corresponding electronic circuit for the model in its integer and fractional order form is designed and implemented in Orcard-Pspice software. The Pspice results are consistent with those from the numerical simulations.