solve errors...
- To: mathgroup at smc.vnet.net
- Subject: [mg43046] solve errors...
- From: sean kim <shawn_s_kim at yahoo.com>
- Date: Sat, 9 Aug 2003 02:57:46 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hello Group.
I don't know if this question has been adressed in the past... If there
was a post about it, I haven't been able to locate it.
here's the problem.
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?
there are 9 equations and 9 variables in this system, shouldn't it
render itself to solution? it appears it isn't.
In[36]:=
Solve[{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]},
{n[t], s[t], t[t], h[t], i[t], k[t], e[t], w[t], x[t]}]
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?
and when you get two solutions for steady state systems, does that mean
there are two steady states?
thanks all in advance for any and all helpful comments.
below is the original system prior to steady state reduction
Out[38]=
\!\(\*
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{
SuperscriptBox["a", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(\(-k1\)\ a[t]\ b[t] + k2\ c[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["b", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(\(-k1\)\ a[t]\ b[t] + k2\ c[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["c", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k1\ a[t]\ b[t] - k2\ c[t] - k3\ c[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["d", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k3\ c[t] - k4\ d[t]\ e[t] + k5\ f[t] + k6\ f[t] -
k8\ d[t]\ i[t] + 9\ j[t] - k13\ d[t]\ k[t] + k14\ l[t]\)}],
",",
RowBox[{
RowBox[{
SuperscriptBox["f", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k4\ d[t]\ e[t] - k5\ f[t] - k6\ f[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["j", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k8\ d[t]\ i[t] - 9\ j[t] - k10\ j[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["p", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(\(-k20\)\ o[t]\ p[t] + k21\ q[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["n", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(\(-k18\)\ m[t]\ n[t] + k19\ o[t] - k23\ n[t]\ s[t] +
k24\ t[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["t", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k23\ n[t]\ s[t] - k24\ t[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["h", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k7\ d[t] - k11\ h[t]\ i[t] + k12\ k[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["k", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k11\ h[t]\ i[t] - k12\ k[t] - k13\ d[t]\ k[t] + k14\
l[t]\)}],
",",
RowBox[{
RowBox[{
SuperscriptBox["l", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k13\ d[t]\ k[t] - k14\ l[t] - k15\ l[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["u", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(\(-k25\)\ m[t]\ u[t] + k26\ v[t] + k27\ v[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["e", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(\(-k16\)\ e[t] - k4\ d[t]\ e[t] + k5\ f[t] -
k28\ e[t]\ i[t] + k17\ w[t] + k29\ x[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["w", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k16\ e[t] + k27\ v[t] - k17\ w[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["g", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k6\ f[t] - k16\ g[t] + k17\ m[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["m", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k16\ g[t] - k17\ m[t] - k18\ m[t]\ n[t] + k19\ o[t] -
k25\ m[t]\ u[t] + k26\ v[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["o", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k18\ m[t]\ n[t] - k19\ o[t] - k20\ o[t]\ p[t] + k21\
q[t]\)}],
",",
RowBox[{
RowBox[{
SuperscriptBox["q", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k20\ o[t]\ p[t] - k21\ q[t] - k22\ q[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["v", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k25\ m[t]\ u[t] - k26\ v[t] - k27\ v[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["x", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k28\ e[t]\ i[t] - k29\ x[t] - k30\ x[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["s", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(\(-k23\)\ n[t]\ s[t] + k24\ t[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["i", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(\(-k8\)\ d[t]\ i[t] - k28\ e[t]\ i[t] - k11\ h[t]\ i[t]
+
9\ j[t] + k10\ j[t] + k12\ k[t] + k15\ l[t] + k29\ x[t] +
k30\ x[t]\)}], ",",
RowBox[{
RowBox[{
SuperscriptBox["r", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}],
"==", \(k22\ q[t]\)}]}], "}"}]\)
=====
when riding a dead horse, some dismount.
while others...
write memoirs on the subject of riding a dead horse.
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