A new hyperjerk dynamical system with hyperchaotic attractor and two saddle-focus rest points exhibiting Hopf bifurcations, its hyperchaos synchronisation and circuit implementation

A new 4D dynamical hyperjerk system with hyperchaos is reported in this work. The proposed nonlinear mechanical system with hyperchaos has two saddle-focus rest points exhibiting Hopf bifurcations. A detailed bifurcation analysis of the new hyperjerk plant with theory and simulations is discussed. As a control application, an integral sliding mode controller has been designed for the global hyperchaos synchronisation of the new hyperjerk system with itself. Finally, a circuit model using MultiSim of the new hyperjerk system with hyperchaos is designed for practical implementation.