Analysis of the Dynamics of Perturbed and Unperturbed Lorenz Systems

Chaotic behavior is a fundamental feature of many nonlinear deterministic systems, leading to a sensitive dependence on initial conditions and unpredictable dynamics. This study investigates chaos in unperturbed and perturbed Lorenz systems using phase portraits, time series analysis, and Lyapunov exponents. The systems were analyzed for parameters σ = 10, ρ = 25, β = 2.667, and perturbation ε = 0.1. Numerical simulations were performed using MATLAB with the fourth-order Runge–Kutta method. Stability analysis of fixed points was conducted alongside graphical and quantitative evaluations. The results show that both systems exhibit at least one positive Lyapunov exponent, confirming the chaotic behavior. However, an increase in the perturbation parameter ε indicates a gradual transition from chaotic dynamics toward more stable behavior. These findings provide insight into the sensitivity and evolution of chaotic systems under perturbations