Duffing Chaotic Oscillator: MATLAB Implementation and Bifurcation Diagram Analysis

This document provides MATLAB implementation code for the Duffing chaotic oscillator and source code for plotting bifurcation diagrams of the Duffing system. The Duffing oscillator is modeled using a second-order nonlinear differential equation, typically implemented with MATLAB's ODE solvers (e.g., ode45) for numerical integration. Key parameters include damping coefficient, nonlinear stiffness, and external forcing amplitude, which are crucial for chaotic behavior generation. The implementation involves setting initial conditions (displacement and velocity) and time parameters, followed by solving the differential equation system. For bifurcation analysis, the code systematically varies control parameters (e.g., driving force amplitude) while tracking Poincaré sections or local maxima to observe period-doubling routes to chaos. The bifurcation diagram plotting utilizes MATLAB's visualization functions (plot, scatter) with proper axis labeling and colormaps to distinguish chaotic and periodic regions. These source codes demonstrate numerical methods for nonlinear system analysis, including phase space reconstruction and Lyapunov exponent estimation techniques. They serve as practical tools for studying chaotic dynamics and bifurcation phenomena in mechanical and electrical oscillator systems. For technical inquiries or implementation support, please contact the author for detailed assistance with parameter tuning and computational methodology.