The forced Duffing oscillator exhibits behavior ranging from limit cycles to chaos due to its nonlinear dynamics. 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.
Here is a link to a Mathematica 6.0 Demonstration concerning the forced Duffing oscillator:
Housam Binous (2022). Forced Duffing Oscillator (https://www.mathworks.com/matlabcentral/fileexchange/16731-forced-duffing-oscillator), MATLAB Central File Exchange. Retrieved .
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