This study investigates a novel symmetry-controlled 5D hyperchaotic hyperjerk system, characterized by the coexistence of hidden chaos and self-excited extreme events, representing an unprecedented feature in nonlinear science. We explore the underlying dynamics of this system, revealing a rich landscape of complex transients and the presence of three positive Lyapunov exponents, which indicate the system’s hyperchaotic behavior. Utilizing numerical simulations (e.g. bifurcation diagrams, Lyapunov exponents’ spectrum, basin of attraction) and analytical techniques, we demonstrate how symmetry properties influence the emergence of chaotic attractors and extreme events within the system. Using an analog simulator of the model under consideration, an experimental study is conducted to verify the predictions of the theoretical analysis. Our findings highlight the intricate interplay between stability and chaos, offering insights into the mechanisms that govern extreme behavior in higher-dimensional dynamical systems. This research not only contributes to the theoretical understanding of hyperjerk systems but also has potential implications for applications in fields such as climate modeling, financial systems, and engineering, where extreme events play a critical role.
Jacques et al. (Thu,) studied this question.