Extreme Events and Hyperchaos in a Special 6D Hyperjerk System

In this paper, we propose a new 6D hyperchaotic hyperjerk system featuring a single nonlinear term in the form of a sinh function, whose argument consists of a linear combination of three state variables. A detailed analysis of the new system is carried out using both analytical and numerical methods, with emphasis on its symmetry properties, computation of dissipation, analysis of equilibrium/rest points, and the route to hyperchaos. It is revealed that the proposed model possesses unique/special nonlinear behaviors, including hyperchaos with three positive Lyapunov Exponents (LEs), Extreme Events (EEs), and an offset boosting property. An appropriate analog circuit emulating the hyperchaotic behavior of the new hyperjerk system is designed using only basic electronic components and two back-to-back diodes to implement the sinh function. Phase portraits obtained from an Arduino-based implementation of the system verify the results of the theoretical investigations. To the best of the authors’ knowledge, the presence of three positive LEs, in addition to the striking feature of EEs reported in this paper, is unique in the relevant literature.