This paper explores classical chaotic systems, including the Lorenz system, Rössler system and Chen System. We systematically investigate the behavior of these chaotic systems by varying parameters. The Lorenz system, known for its butterfly-shaped attractor, showcases the intricate dynamics resulting from its sensitivity to initial conditions. The Rössler system, featuring a twisted double-scroll attractor, is analyzed for its chaotic behavior and parameter-dependent properties. The Matlab-based analysis allows for a comprehensive examination of strange attractors, providing visualizations that enhance our understanding of their complex structures. By systematically altering parameters, we observe the evolution of attractors, gaining insights into how changes in system conditions influence their dynamics. This exploration contributes to a deeper comprehension of chaos in nonlinear dynamical systems. The study underscores the significance of Matlab simulations in unraveling the complexities of classical chaotic systems, offering a valuable tool for researchers and practitioners seeking to analyze and understand chaotic dynamics in various scientific and engineering applications. Additionally, the paper presents a spectral analysis of Lorenz system utilizing FFT and wavelet decomposition techniques