On Mon, 3 Mar 2003, Stavros Macrakis wrote:
> James, give us some guidance here. What are you looking for? A
> qualitative characterization of the solutions? A fast way of
> calculating solutions for particular parameter values? What are the
> interesting ranges of the parameters? Which are the interesting
> solutions? -- presumably only the ones with Bmin<B<Bmax and Fmin<F<Fmax,
> but in your example, one solution is near Bmin, two are near Bmax, and
> one is in between. Are these all interesting solutions?
This is actually a homework problem for a course in mathematical
modelling. It's a problem in population growth: given two species with
specified populations, growth rates & minimum viable populations (the
various parameters in my first message), find all the equilibrium points,
and determine whether they're stable or unstable.
For this particular problem a numeric solution is acceptable (and indeed I
could have hacked out a C program to do so in short order), but since one
goal of the course is to learn how to use symbolic math programs, I wanted
to try the symbolic route too. So now I've at least learned that in this
instance, a symbolic solution isn't really practical :-)
Thanks,
James