x = x_0 y = dx_0 d_x = y d_y = mu * (1 - x**2) * y - x
Note the blank line between the initial conditions and the expression for the derivatives. This is the representation of the form using
y as the derivative of
x. The integration variable in QSoas is the time
t. You can learn more about how to specify differential equations in QSoas from the manual. The game is now simply to use fit-ode to launch the fit interface, but before that, one needs data to serve as a template, generated using generate-buffer:
QSoas> generate-buffer 0 100 1 QSoas> fit-ode vanderpol.ode
Now, the fit interface looks like this:
You can play around with the parameters, and in particular the value of
mu... For every modification, hit the Update button, or just Ctrl+U, to see the effect. For data you'd wish to take a closer look at, use the Push current to stack action from the Data... menu, which creates new buffers on the stack. A nice thing is that QSoas keeps the fit parameters as meta-data, which you can see later on using show:
muin the terminal above ?
This feature of QSoas makes it easy to quickly explore the effect of the parameters of a model on the shape of the resulting curve. I have used that very heavily in my research, I hope others will find it useful too. Enjoy !