Analyze the non-linear Duffing equation with this tool. The Ejs Duffing Attractor model computes the solutions to the non-linear Duffing equation, which reads, x'' + 2 x' - x (1 - x2) = f cos( t), where each prime denotes a time derivative. The simulation displays a three-dimensional plot of phase space versus angle and three Poincare plots separated by angles of 2 /3. 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 ? x' - x (1-x2) = f cos ?t where each ' denotes a time derivative.
You can select below the parameters ? and f, as well as the initial conditions for the elongation x and the velocity v = x'.
The unit time is 1/ ? (so that ? = 1).
Since the equation is not autonomous, the full phase space is that of triplets (t, x, v) or, since t only appears in the cosinus, (?t mod 2p, x, v). The simulation will display a projection of the orbit in a space in which the phase ?t mod 2p coils around an axis.
The simulation will also display 3 stroboscopic Poincar?sections defined by the conditions ?t mod 2p = f, f+2/3p, f+4/3p.
The point of view of the three-dimensional projections can be changed with the cursors or the mouse.
Each whole image can be moved with the mouse while pressing Ctrl.
To change the zoom in the projections, press Shift when moving up or down the mouse pointer.
Put the mouse pointer over an element to get information about it.

Requirements:
* Java

The license of this software is Freeware, you can free download and free use this calculator software.