MATLAB Bifurcation Analysis of Duffing System

This article presents a MATLAB implementation for bifurcation analysis of the Duffing system. While this program serves as a practical starting point for beginners, it opens pathways for deeper exploration of the system's mathematical model and physical phenomena. The code typically involves numerical integration methods like Runge-Kutta algorithms (e.g., ode45 function) to solve the Duffing equation: d²x/dt² + δdx/dt + αx + βx³ = γcos(ωt). Users can extend the analysis to study chaotic behavior through Lyapunov exponent calculations or implement advanced numerical simulations exploring parameter spaces. Furthermore, comparative studies with other physical systems (e.g., Van der Pol oscillator) can be coded using similar MATLAB framework to better understand the Duffing system's unique characteristics and applications. Through systematic parameter variation and phase portrait generation, researchers can gain comprehensive insights into bifurcation patterns and nonlinear dynamics.