Environmental Engineering Reference
In-Depth Information
The result is a 'flowpath' in the phase space towards the steady state, a so-called
trajectory
. In the phase space such lines are called trajectories. In order to obtain
a more illustrative figure, we chose several starting positions around the equilibrium
solution. One obtains:
The complete code is included in the accompanying software under the name
'phasediag.m'.
The graphical output of the M-file is depicted in Fig.
18.8
. The graphic was
extended manually by arrows in order to indicate the temporal direction of the
trajectories. A textbox was added close to the position of the stable equilibrium.
Figures similar to the one depicted arise, whenever two variables are plotted in
the vicinity of a stable equilibrium. Obviously, the equilibrium is approached
differently from different angles, which is a result of the different eigenvalues.
For the more seldom case of equal eigenvalues, the resulting figure looks differ-
ently, although the qualitative behavior remains the same. In case of an unstable
