predprey - plot the phase space of a predator-prey system
[-width integer] [-height integer] [-skip integer]
[-points integer] [-alpha double] [-delta integer]
[-dt double] [-x0 double] [-y0 double] [-z0 double]
[-data] [-xp string] [-yp string] [-factor double]
[-inv] [-mag integer] [-term string]
The phase space of a three species predator-prey system,
which is described by the three differential equations
dx/dt = x * (1.1 - x / 2 - y / 2 - z / 10),
dy/dt = y * (-0.5 + x / 2 + y / 10 - z / 10), and
dz/dt = z * (alpha + 0.2 - alpha * x - y / 10 - z / 10),
is plotted according to the specified parameters. Valid
arguments passed with the -xp and -yp options can be any
one of x(t), y(t), z(t), x(t-delta), y(t-delta), or z(t-
delta). Thus, the displayed plot can take the form of a
state space plot or a delayed coordinate plot.
Width of the plot in pixels.
Height of the plot in pixels.
Number of initial points to skip.
Number of points to plot.
Value of the alpha parameter.
Time delay term.
Initial X value.
Initial Y value.
Initial Z value.
-data Don't plot, but print points.
X-coordinate for plot.
Y-coordinate for plot.
Auto-scale expansion factor.
-inv Invert all colors?
How to plot points.
The plot region is determined by the points that are ini-
tially skipped. If this number is too small (i.e., it is
not very representative of the range of the plotted val-
ues), then you may need to increase the number specified
by the -skip option. Alternatively, you can adjust the
value given to -factor, which simply fractionally
increases the border of the plot.
The program uses a second-order Euler's method to perform
the numerical integration, which is sufficient for simple
tasks such as this.
No sanity checks are performed to make sure that any of
the options make sense.
Copyright (c) 1997, Gary William Flake.
Permission granted for any use according to the standard
GNU ``copyleft'' agreement provided that the author's com-
ments are neither modified nor removed. No warranty is
given or implied.