Scalar modeling and analysis of a 3D biochemical reaction model

For many systems it is advantageous if analysis and modeling can be accomplished from a scalar time series because this greatly facilitates the experimental setup. Moreover, in real-life systems it is hardly true that all the state variables are available for analysis and modeling. Since the late 1980s, techniques have been put forward for building mathematical models from a scalar time series. One of the objectives of this paper is to verify if it is possible to obtain global non-linear models (non-linear differential equations) from scalar time series. Such data are obtained using a model of biochemical reaction with aperiodic (chaotic) oscillations as recently observed in the case of a glycolytic reaction (Nielsen, K., Sorensen, P.G., Hynne, F., 1997. Chaos in glycolysis. J Theor. Biol. 186, 303–306.). The main objective, however, is to investigate which state variable is more convenient for the task in practice. It is shown that observability indices seem to quantify quite well which variable should be preferred as the observable. The validity of the results are established performing rigorous topological analysis on the original system and the obtained models. The influence of noise, always present in experimental time series, on the dynamics underlying such a system is also investigated.