Re: not linear homogeneus differential equation system... too complicated for mathmeatica... maybe only for me! :)
- To: mathgroup at smc.vnet.net
- Subject: [mg41795] Re: not linear homogeneus differential equation system... too complicated for mathmeatica... maybe only for me! :)
- From: "Alessandro" <TheOpps75 at yahoo.it>
- Date: Fri, 6 Jun 2003 09:50:28 -0400 (EDT)
- Organization: GWDG, Goettingen
- References: <bbmtpp$hf$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
ok... I've just renamed constant because they are combinations of other parameters. No... no hidden biology is a generalized schema of transition between electronic states for a population of donor/acceptor fluorescent probes. So... photophysics. Well, I'm able to solve easier schema. One molecule manually, two molecules by mathematica, but I start obviously to get problem when I insert a non-linearity. I'm a physicist but it is a long time I don't play with this kind of problems. However I'm interested in the general solution because I want to study the different behaviour of the system in function of these parameters. With easier schema it is possible retrieve the true analytical general solution so I was wondering if also with this more complex one it is. I just need to decide now if solve numerically the model with different initial parameters and rate constant and "fit the properties of the solutions" or make directly simulations... If interested as soon as I'll found a solution I'll post it, but I'm making this in the free time so it will take a long time :)))))) Thanks for the suggestions regarding the numerical integration functions Alessandro "sean kim" <shawn_s_kim at yahoo.com> wrote in message news:bbmtpp$hf$1 at smc.vnet.net... > 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. > > __________________________________ > Do you Yahoo!? > Yahoo! Calendar - Free online calendar with sync to Outlook(TM). > http://calendar.yahoo.com >