Re: not linear homogeneus differential equation system... too complicated for mathmeatica... maybe only for me! :)
- To: mathgroup at smc.vnet.net
- Subject: [mg41763] Re: [mg41718] not linear homogeneus differential equation system... too complicated for mathmeatica... maybe only for me! :)
- From: sean kim <shawn_s_kim at yahoo.com>
- Date: Wed, 4 Jun 2003 08:34:44 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
lol another biologist i presume?
appears the system is from some kind of network diagram. perhaps you
woul dbe kind to share with us?
I have agree with dr Hollis in that the system should be solved using
using NDSolve.
as far as i can tell, to have a solution to a given differential
equation means to find the a function or values of functions that
stisfy the contraint given the differential eqaution.
how would you do this for a system of differential equations? I guess
it might be possible to have it once to decompose the system into a
single ODE...
for now it seems like the best way to "solve" your system and get an
intelligible answer or graphs is to use NDSolve and estimate the
solution.
also are your initial conditions are kinda weird. most ppl seem to use
initial conditions that somehow costrained by a system. if you want to
use NDSOlve you need to decide on such IC's.
i'm a biologist myself, so it must be hard starting out in this new
field of ODE's. so here're some hints.
1. first you need the coefficients as Dr hollis mentioned. those are
your A, B, C, E, F, G. They should be kinetic rates of the protein
binding, if i'm right in thinking this is a biological network.
2. then you need the initial conditions. those are your s[0] == s0,
a[0] == a0, b[0] == 0, u[0] == 0., last two are fine. but you need
nuemrical values for s[0] and a[0]. this is where soem decision needs
to made unless you have these measurements available.
3. once you have numbers for things mentioned above. then you can use
NDSolve as follows. just for the sake of the example i decided to use
soem random and nosensical numbers as folows.
{ A -> 0.1, B -> 0.01, C -> 0.001, E -> 0.0001, F -> 0.00001, G ->
0.00001, s0 -> 10, a0 -> 20}
then the numerical system looks liek this.
In[6]:=
numericalsystem = {s'[t] == -A*s[t] + B*u[t],
u'[t] == A*s[t] - (E + C*a[t] + B)*u[t],
a'[t] == F*b[t] - C*a[t]*u[t],
b'[t] == C*a[t]*u[t] - (G + F)*b[t],
s[0] == s0, a[0] == a0, b[0] == 0, u[0] == 0} /. { A -> 0.1, B ->
0.01, C -> 0.001, E -> 0.0001, F -> 0.00001, G -> 0.00001, s0 -> 10, a0
-> 20}
and then
In[7]:=
soln = NDSolve[numericalsystem, {s[t], u[t], a[t], b[t]}, {t, 0, 10}]
gives the following
Out[7]=
{{s[t] -> InterpolatingFunction[{{0., 10.}}, "<>"][t],
u[t] -> InterpolatingFunction[{{0., 10.}}, "<>"][t],
a[t] -> InterpolatingFunction[{{0., 10.}}, "<>"][t],
b[t] -> InterpolatingFunction[{{0., 10.}}, "<>"][t]}}
then the following graphs them.
In[11]:=
Plot[Evaluate[s[t] /. soln], {t, 0, 10}]
Plot[Evaluate[u[t] /. soln], {t, 0, 10}]
Plot[Evaluate[a[t] /. soln], {t, 0, 10}]
Plot[Evaluate[b[t] /. soln], {t, 0, 10}]
enjoy and good luck.
tell us what network above is for. i would love to know what people are
working on.
sean from UCIrvine.
=====
when riding a dead horse, some dismount.
while others...
form a committee to examine the deadness of the horse, then form an oversight committee to examine the validity of the finding of the previous committee.
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