Duffing Equation Solver with MATLAB Implementation

This compact program solves the Duffing equation using MATLAB's numerical computation environment. The core implementation employs differential equation solvers like ode45 or ode15s to numerically integrate the nonlinear system. Beyond plotting solution trajectories, the program incorporates parameter tuning functionality through customizable input variables, enabling users to modify stiffness coefficients, damping parameters, and excitation forces for behavioral studies. The code includes Lyapunov exponent calculation routines and sensitivity analysis tools to assess solution stability under parameter variations. Comprehensive documentation embedded in the script provides usage guidelines, including function calls for data output and visualization commands for phase portraits and time-domain plots. The program serves as an educational framework for understanding Duffing oscillator dynamics, with modular code structure allowing extensions for bifurcation analysis and chaos detection algorithms.