Phase Space Reconstruction Program for Chaotic Time Series of the DUFFING Equation

This document presents an implementation focused on the Duffing equation, which represents a fundamental nonlinear oscillation system widely studied in dynamical systems theory. The program performs phase space reconstruction from chaotic time series data, a critical technique for analyzing dynamical system behavior without prior knowledge of governing equations. Through phase space reconstruction analysis, we can extract fundamental characteristics of the Duffing equation's behavior and its impact on system dynamics. The implementation typically involves key computational steps including time-delay embedding using Takens' theorem, determination of optimal embedding parameters through false nearest neighbors analysis, and trajectory visualization in reconstructed phase space. This reconstruction program enables deeper investigation of the Duffing equation's complexity and practical applications, with potential extensions to Lyapunov exponent calculation and attractor dimension estimation for complete nonlinear system characterization.