Research and Simulation of Synchronization Techniques for Lorenz Chaotic Systems

This paper investigates the research and simulation of synchronization techniques for Lorenz chaotic systems. Following in-depth analysis, we present three synchronization approaches: PC-based chaos synchronization (implementing coupling control through parameter matching algorithms), linear state feedback synchronization (utilizing real-time state variable correction with matrix gain optimization), and observer-based synchronization (designing state estimators using Lyapunov stability criteria). The discussion includes comparative analysis of each method's advantages and limitations, along with their practical implementation potential and constraints. The paper aims to enhance readers' understanding of synchronization mechanisms in Lorenz chaotic systems through detailed algorithmic explanations and simulation scenarios. Code implementation typically involves solving differential equations using Runge-Kutta methods while maintaining synchronization through error minimization functions.