Eur. Phys. J. Plus (2019) 134: 499
https://doi.org/10.1140/epjp/i2019-13005-5

Regular Article

Dynamics of a new hyperchaotic system and multistability

¹ Faculty of Defence Science and Technology, Universiti Pertahanan Nasional Malaysia, Sungai Besi, Malaysia
² Information Technology College, Department of Communications Technologies Engineering, Imam Ja’afar Al-Sadiq University, Baghdad, Iraq
³ Centre for Defence Foundation Studies, Universiti Pertahanan Nasional Malaysia, Sungai Besi, Malaysia
⁴ Cyber Security Centre, Universiti Pertahanan Nasional Malaysia, Sungai Besi, Malaysia
⁵ Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
⁶ Malaysia-Italy Centre of Excellence for Mathematical Science, University Putra Malaysia, Serdang, Malaysia

^* e-mail: santoban@gmail.com

Received: 6 August 2019
Accepted: 16 September 2019
Published online: 9 October 2019

Abstract

In this paper, a new 4D hyperchaotic system is proposed. By boosting a trigonometric function into a single variable, the system produces different multistable regions. Bifurcation diagrams and cross-section of basins can quantify the presence of coexisting attractors. Furthermore, a nonlinear controller is implemented, which can shift the coexisting attractor in the negative region in the phase space and merge it to the positive region, for a threshold value of the control parameter. It has also been noticed that complexity increases with the addition of the nonlinear controller, when the coexisting attractors shift to the positive region in the phase space.