Duffing Equation Chaos Analysis

This source code provides a complete implementation for analyzing chaos in Duffing equations. The program enables visualization of chaotic phase portraits and computation of the maximum Lyapunov exponent through sophisticated numerical algorithms. The Duffing equation represents a fundamental mathematical model describing nonlinear oscillations, and this implementation allows researchers to thoroughly investigate its chaotic characteristics. The core implementation utilizes fourth-order Runge-Kutta methods for numerical integration of the Duffing system. Key functions include phase space reconstruction, time series analysis, and Lyapunov exponent calculation using the Wolf algorithm for chaos quantification. Users can modify system parameters and initial conditions through adjustable input variables to observe diverse chaotic behaviors under different configurations. The code architecture supports parameter sweeps and bifurcation analysis, enabling systematic exploration of the transition from periodic to chaotic regimes. Visual output modules generate high-quality phase portraits and time series plots, while the Lyapunov calculation module provides quantitative measures of chaos sensitivity. This implementation serves as an excellent educational and research tool for understanding chaotic systems, offering both visual demonstrations and quantitative analysis of nonlinear dynamics. Researchers can extend the codebase for additional chaos indicators or apply it to related nonlinear oscillator systems.