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two coupled differential equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121182] two coupled differential equations
  • From: Mark.Musters at leadpharma.com
  • Date: Sat, 3 Sep 2011 08:04:09 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

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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