Bifurcations and chaos dynamics of a hyperjerk system with antimonotonicity
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Bifurcations and chaos dynamics of a hyperjerk system with antimonotonicity Lishuang Jiang1, Jing Li1,a
, Wei Zhang2
1 Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124,
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, Beijing 100124, China Received: 6 June 2020 / Accepted: 16 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 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.
1 Introduction Chaos arising in engineering applications has been attracting much attention in the field of nonlinear sciences. Since Lorenz [1] first found the chaotic attractor in a three-dimensional autonomous ordinary differential equation, chaos theory has been developed and intensively studied in the past five decades. Chaos is defined as ‘a deterministic but unpredictable state of motion’ in nonlinear sciences. It is remarkable that the chaotic behavior is highly sensitive to initial conditions [2,3]. A small change in the initial conditions of dynamical system causes wide difference of trajectories. In the era of information explosion, the innovation of information technology makes the problem of information security increasingly prominent. The information transmitted through the Internet and mobile communication network is likely to be monitored, captured, duplicated or even tampered by others, which seriously threatens the security of personal privacy, national economy and military secrets. Secure communications based on high-dimensional chaotic system have the advantages of better confidentiality, larger storage capacity and information processing capacity and stronger robustness [4]. In
a e-mail: [email protected] (corresponding author)
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Eur. Phys. J. Plus
(2020) 135:767
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