Forced Duffing Oscillator

The forced Duffing oscillator exhibits behavior ranging from limit cycles to chaos due to its nonlinear dynamics. The governing equation is , with , , , , , and . When the periodic force () that drives the system is large, chaotic behavior emerges and the phase space diagram is a strange attractor. In that case the behavior of the system is sensitive to the initial condition. In order to plot a Poincaré section, take one data point from phase space per period of the driving force. The Poincaré section is a complicated fractal curve when the phase diagram is a strange attractor. The Poincaré section is a single point when the phase space diagram is a limit cycle.