Judging Chaotic Phenomena and MATLAB Implementation with Code Descriptions

In the following text, I will describe the criteria for judging chaotic phenomena and provide the source code for simulating this process using MATLAB. Chaos represents unpredictable behavior observable in numerous natural phenomena such as meteorology, biology, chemistry, and geology. Chaotic phenomena find wide applications across disciplines including biology, chemistry, physics, and engineering. This article focuses on demonstrating how to program chaotic process simulations using MATLAB, with implementation details covering key functions like ode45 for differential equation solving and Lyapunov exponent calculation algorithms. Through simulation analysis, we can observe characteristic patterns of chaotic systems including sensitivity to initial conditions and fractal structures. The source code will include detailed step-by-step explanations with comments on numerical methods such as Runge-Kutta integration and phase space reconstruction techniques, enabling easy replication and adaptation for research purposes. This article aims to facilitate deeper understanding of chaotic phenomena and provide practical tools for research applications.