MATLAB Implementation of Chen's Chaotic Time-Delay System

In this article, we present a MATLAB implementation methodology for Chen's chaotic time-delay system. The Chen chaotic system represents a three-dimensional nonlinear dynamical system that finds extensive applications in scientific research, including image encryption, signal processing, and communication systems. We will provide a comprehensive discussion on modeling the Chen chaotic system using MATLAB, with particular emphasis on implementing the system's chaotic behavior through numerical integration techniques. The implementation involves defining system parameters, initial conditions, and employing ODE solvers like ode45 to simulate the system's evolution. We will examine key MATLAB functions for phase space visualization and Lyapunov exponent calculation to characterize chaotic properties. Additionally, we introduce analytical tools and techniques to help developers better understand the system's operational mechanisms, including bifurcation analysis and sensitivity to initial conditions. Through code examples demonstrating parameter variation effects and trajectory plotting, this article aims to provide readers with a deeper understanding of Chen's chaotic system and its potential in practical engineering applications.