Qualitative analysis of a novel 4D hyperchaotic system and its chaos synchronization via active, adaptive, and sliding mode control

This study introduces a brand-new, four-dimensional hyperchaotic system and provides a full analysis of its dynamical characteristics. Time series, phase portraits, Poincaré maps, bifurcation diagrams, estimating the Lyapunov exponents, and determining the Kaplan–Yorke dimension are all used to examine the system. Additionally, the system’s equilibrium points are located and their stability is explored. Through the use of active, adaptive, and sliding-mode control approaches, we have also synchronized the newly introduced system. The Lyapunov stability theory and Vaidyanathan’s theorem are the foundations upon which the controllers are built to guarantee synchronization between the systems. Finally, MATLAB-based numerical simulations are used to verify the theoretical findings.