Abstract
In this work, we report a new 4D chaotic hyperjerk system and present a detailed dynamic analysis of the new system with Lyapunov exponents, bifurcation plots, etc. We find that the new hyperjerk system exhibits multistability and coexisting chaotic attractors. The hyperjerk system has a unique saddle-focus rest point at the origin, which is unstable. This shows that the new chaos hyperjerk system has a self-excited chaotic attractor. As an application of backstepping control, we obtain new results for the global chaos complete synchronisation of pair of chaotic hyperjerk systems. A circuit model using MultiSim of the new chaotic hyperjerk system is designed for applications in practice. Finally, an FPGA-based implementation of the new chaotic hyperjerk dynamical system is performed by applying two numerical methods and their corresponding hardware resources are given.
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