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Re: two coupled differential equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121297] Re: two coupled differential equations
  • From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
  • Date: Thu, 8 Sep 2011 05:25:49 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <j3t57m$56h$1@smc.vnet.net>

First, the de for x1 is not coupled to that for x2; so, solve it 
separately. You can do this and then find the optimum k1 and initial 
condition on x1 (you didn't specify this). Then proceed to that for x2 
(numerical solution only). This will not necessarily give you the global 
best fit to the parameters, but at least it is a start.

I will send you a notebook separately that gives my attempt.

Kevin

On 9/3/2011 8:06 AM, Mark.Musters at leadpharma.com wrote:
> Hi
>
> I have two coupled differential equations, for which I would like to
> derive the parameter values by fitting them on a data set.
>
> The differential equations have the following form:
>
> x1'[t] == -k1*x1[t]
> x2'[t] == k2*x1[t]-k3*x2[t]/(k4+x2[t])
>
> The experimental time-series data has the following form
> t== {0,1,4,8,12,24}
> x1 == {10,9,5,3,1,.1}
> x2 == {2,4,5,7,9.1,11}
>
> The examples I can find with FindFit are aimed at a single differential
> equation, so I was wondering how I can assign the data to the
> corresponding state variable and perform a parameter estimation to get
> an estimate for parameters k1, k2, k3 and k4.
>
> It would help me a lot.
>
> Many thanks in advance,
> Mark




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