Numerical Computation of Six Important Chaotic Models Including Lorenz System

In this article, we present numerical computations of six important chaotic models using MATLAB mathematical software, simulating unique properties of various chaotic systems. These properties include chaotic attractors, period-doubling bifurcations, sensitivity to initial conditions, phase portraits, and bifurcation diagrams. Through observation and analysis of these characteristics, we explore the fundamental nature of chaotic phenomena. Our implementation leverages MATLAB's differential equation solvers (ode45 for non-stiff systems, ode15s for stiff systems) with appropriate step-size control to maintain numerical accuracy. Additionally, we employ specialized visualization techniques including 3D plotting functions (plot3) for attractor visualization and custom algorithms for bifurcation diagram generation. Furthermore, we discuss practical applications of these models and their significance in physics, chemistry, and biological sciences, demonstrating how parameter variations in the governing equations can be systematically analyzed using MATLAB's parameter sweeping capabilities.