Re: solve errors...
- To: mathgroup at smc.vnet.net
- Subject: [mg43062] Re: [mg43046] solve errors...
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Sun, 10 Aug 2003 01:46:50 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Saturday, August 9, 2003, at 02:57 AM, sean kim wrote:
> Please consider the following reduced steady state system which is
> generated from a larger ODE system. with some assumptions, the larger
> system reduces down to below. ( original system is posted at the end of
> the message)
>
> { 0 == -k23 n[t] s[t] + k24 t[t],
> 0 == k23 n[t] s[t] - k24 t[t],
> 0 == -k11 h[t] i[t] + k12 k[t],
> 0 == k11 h[t] i[t] - k12 k[t],
> 0 == -k16 e[t] - k28 e[t] i[t] + k17 w[t] + k29 x[t],
> 0 == k16 e[t] - k17 w[t],
> 0 == k28 e[t] i[t] - k29 x[t] - k30 x[t],
> 0 == -k23 n[t] s[t] + k24 t[t],
> 0 == -k28 e[t] i[t] - k11 h[t] i[t] + k12 k[t] + k29 x[t] + k30
> x[t]}
>
> as far as i understand it, given a number of algebraic equations, with
> equal number of variables, then the system should be solvable in terms
> of the variables. Am I not correct?
Afraid not. For example, a nonhomogeneous linear system my fail to have
a solution if the coefficient matrix is singular.
> <snip>
> Solve::"svars": "Equations may not give solutions for all \"solve\" \
> variables."
> Out[36]=
> \!\({{t[t] -> \(k23\ n[t]\ s[t]\)\/k24, w[t] -> \(k16\ e[t]\)\/k17,
> k[t] -> 0, x[t] -> 0, i[t] -> 0}, {t[t] -> \(k23\ n[t]\
> s[t]\)\/k24, w[t] -> 0, k[t] -> \(k11\ h[t]\ i[t]\)\/k12, x[t] -> 0,
> e[t] ->0}}\)
>
> Why is this happening? is there a way to fool the mathematica to solve
> for the variables?
One can sometimes help things along by eliminating some of the
variables "manually." And if you have some idea where a solution might
be, you could try using FindRoot.
>
> and when you get two solutions for steady state systems, does that mean
> there are two steady states?
Certainly. Although some may not be meaningful, depending on the
application. For instance, you might want only nonnegative solutions,
and you probably want only real ones.
-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis