Nonlinear Dynamics and Stability Analysis of an 8D Lorenz-Type Hyperchaotic System: Lyapunov Exponents and Bifurcation Study

Résumé

The nonlinear dynamics and stability properties of an 8D Lorenz-type hyperchaotic system are investigated in detail in this paper. Focusing on the appearance of multiple positive Lyapunov exponents, we explore periodic and hyperchaotic behaviors dependence on the system parameters. Numerical simulations are employed to illustrate the inherent unpredictability of the system, which is linked to complex attractor geometries and high sensitivity to initial conditions. Bifurcation studies provide additional insight into the routes to anarchy and identify important crisis points. The Jacobian method is also used to investigate stability of the analysis, and which eliminates other variables of less importance for the behaviour of the system. Dissipative behavior of the system is demonstrated and applications to secure communications and control engineering are proposed. This paper combines the theoretical justification with numerical simulation results so that a systematic approach to analyzing high-dimensional chaotic systems under parametric perturbations and external excitations can be offered.