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Crash course in
DsTool
The Models menu contains the models that you can load into
dstool_tk. By default dstool_tk load the Lorenz system.
The Panels menu contains the computational options, a selection
of which is described below.
- Two-D
- This window shows two-dimensional projections of the phase space
cross the parameter space (and extra functions defined by the
user). By default the first two variables of the system are
shown. Click with the left mouse button in this window to select an
intial condition (other variables and parameters remain unchanged). A
click with the middle mouse button will then start the computation of
an orbit using the selected initial conditions.
- Selected
- All initial conditions, both parameters and variables, are given
in this window. Once you computed an orbit, the final point will be
shown in the column on the right. Copy final to initial results
in copying this last point to be the initial condition. For example,
check the numerical sensitivity by computing a forward orbit, copying
the final point, and subsequently computing the backward orbit. The
two orbits should be identical, but typically, they are not.
- Orbits
- The Orbits window shows the constants used to compute
forward and backward orbits. The default is 5000 integrations with
step size 0.01 plotting every point starting from the selected
one. Forward orbits are computed by clicking on Forwards and
continued by clicking Continue after that. Going backward,
click Backwards, results in computing the backward orbit
starting from the initial condition in the Selected window
(under the Panels menu).
"Strobing at the forcing frequency" as suggested in the parametrically
forced damped pendulum, is done by changing Fixed steps to
Poincare section. In the model file an extra function called
Period is defined that is 0 exactly at full periods of the
forcing. Select this function, requesting it to be equal to 0, by
clicking on the little square button next to it. Computing 5000 points
on the Poincare section typically takes quite a long time; you may
want to try 500 points or so first. On the other hand, Max steps
between sections should be relatively large; 5000 is fine.
- Fixed points
-
Finding fixed points should be straightforward. Note that dstool_tk
cannot find fixed points of a Poincare sections. Fixed points that are
found are printed in the window from which you started dstool_tk,
including information on the eigenvalues and the type.
One-dimensional manifolds can be added. You probably want to increase
the stable manifold steps and unstable manifold steps to
2000 or more.
Written by Hinke Osinga
Last modified: Tue Mar 30 18:48:25 1999