Eur. Phys. J. Plus (2020) 135: 767
https://doi.org/10.1140/epjp/s13360-020-00786-x

Regular Article

Bifurcations and chaos dynamics of a hyperjerk system with antimonotonicity

¹ Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, 100124, Beijing, China
² Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Faculty of Materials and Manufacturing, Beijing University of Technology, 100124, Beijing, China

^b leejing@bjut.edu.cn

Received: 6 June 2020
Accepted: 16 September 2020
Published online: 27 September 2020

Abstract

In this paper, the bifurcations and chaos dynamics of a hyperjerk system with antimonotonicity are investigated via the analytical methods and numerical calculations. We discuss the local stabilities of equilibrium points and its bifurcations depending on parameters. The predicted bifurcations of periodic orbits including flip bifurcation, fold bifurcation and symmetry-breaking bifurcation are investigated. The accurate relations between parameters are established to identify the type of bifurcation appearing in system efficiently. Such simple system has very abundant dynamical behaviors, including period-doubling cascades route to chaos, intermittency regime, antimonotonicity and boundary crisis. The coexisting dynamics is confirmed effectively by using basins of attraction, bifurcation diagram, Lyapunov exponent spectrum and phase portraits. The research reveals the richness and complexity of potential stable states to which this chaotic hyperjerk system can evolve and offers flexibility in realization of various applications including secure communications.