osc

The system models an oscillator and is given in Karnaukhov et al. (2007).

The system consists of 3 dependent variables X₁...X₃ and 6 parameters k₁...k₆.

X1'(t) = k1*X2(t)

X2'(t) = -k2*X1(t) + k3*X2(t) - k2*X2(t)*X3(t)

X3'(t) = k5*X1(t)2 - k6*X3(t)

The following parameter values are used: k=[0.9,0.9,1.0,1.0,0.6,0.6,0.8].

The system specification in the same format as the problem: osc.

The system specification in SBML format: osc.xml.

A simple Matlab script for simulating the system is given in osc.m.

About the problems

The problem osc1 includes perfect data and is similar to a problem discussed in Karnaukhov et al. (2007).

The problem osc2 considers the same experiments as in osc1 but with the addition of Gaussian noise with 3% standard deviation relative to the particular experimental value. 3 points are sampled at t=0 and the average value is considered.

Reference

Karnaukhov,A.V., Karnaukhova,E.V., Williamson,J.R. (2007) Numerical Matrices Method for nonlinear system identification and description of dynamics of biochemical reaction networks. Biophys J., 92, 3459-73. PMID:17350997