Study the non-linear Duffing equation with this utility. Duffing Oscillator Model is a simple, Java based application designed to compute the solutions to the non-linear Duffing equation, which reads, x + 2γx - x (1 - x2) = f cos(ωt), where each prime denotes a time derivative. The simulation displays the solution as well as the phase space and Poincare plots, and energy diagram. 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.

Ejs Duffing Oscillator model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Duffing.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.

Duffing equation
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' (x and v can also be selected by moving with the mouse the point on the display Phase space).
The unit time is 1/ ? (so that ? = 1).
For information on other elements, put over them the mouse pointer to get a tooltip.
It is possible to draw the x(t) evolution, the phase space, any stroboscopic Poincar section (defined by a condition in the form ?t mod 2p = f) and the evolution of the mechanical energy (when f = 0, one gets with the latter the graph of the potential energy in red).

Requirements:
* Java

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