NAME

       predprey - plot the phase space of a predator-prey system

SYNOPSIS

       predprey -help
         or
       predprey
              [-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]

DESCRIPTION

       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.

OPTIONS

       -width integer
              Width of the plot in pixels.

       -height integer
              Height of the plot in pixels.

       -skip integer
              Number of initial points to skip.

       -points integer
              Number of points to plot.

       -alpha double
              Value of the alpha parameter.

       -delta integer
              Time delay term.

       -dt double
              Time step.

       -x0 double
              Initial X value.


       -y0 double
              Initial Y value.

       -z0 double
              Initial Z value.

       -data  Don't plot, but print points.

       -xp string
              X-coordinate for plot.

       -yp string
              Y-coordinate for plot.

       -factor double
              Auto-scale expansion factor.

       -inv   Invert all colors?

       -mag integer
              Magnification factor.

       -term string
              How to plot points.

MISCELLANY

       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.

BUGS

       No sanity checks are performed to make sure  that  any  of
       the options make sense.

AUTHOR

       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.