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Application details

The Ejs Duffing Baker’s Map model computes the solutions to the non-linear Duffing Equation, which reads, x” + 2γ x’ – x (1 – x2) = f cos(ω t), where each prime denotes a time derivative. The simulation displays N2 Poincare plots each separated by the same phase angle. The evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item.

This simulation explores the Duffing equation, which reads (in dimensionless variables) as follows: x” + 2 γ x’ – x (1-x2) = f cos ωt where each ‘ denotes a time derivative.

You can select below the parameters γ and f, as well as the initial conditions for the elongation x and the velocity v = x’.
The unit time is 1/ ω (so that ω = 1).
For information on other elements, put over them the mouse pointer to get a tooltip.
The simulation will display N2 stroboscopic Poincar sections defined by a series of conditions in the form ωt mod 2π = φ + 2 n π/N2 for n = 0, 1, , N2-1 (from left to right and then from top to bottom)