Elimination of the initial value parameters when identifying a system close to a Hopf bifurcation

G. Cedersund. IEE Proceedings - Systems Biology, Nov 2006, Volume 153, Issue 6, p. 448-456.


One of the biggest problems when performing system identification of biological systems is that it is seldom possible to measure more than a small fraction of the total number of variables.If that is the case, the initial state, from where the simulation should start, has to be estimated along with the kinetic parameters appearing in the rate expressions. This isoften done by introducing extra parameters, describing the initial state,and one way to eliminate them is by starting ina steady state. We report a generalisation of this approachto all systems starting on the centre manifold, close toa Hopf bifurcation. There exist biochemical systems where such datahave already been collected, for example, of glycolysis in yeast.The initial value parameters are solved for in an optimisationsub-problem, for each step in the estimation of the otherparameters. For systems starting in stationary oscillations, the sub-problem issolved in a straight-forward manner, without integration of the differentialequations, and without the problem of local minima. This ispossible because of a combination of a centre manifold andnormal form reduction, which reveals the special structure of theHopf bifurcation. The advantage of the method is demonstrated onthe Brusselator.


  • Gunnar Cedersund, Fraunhofer-Chalmers Centre.

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