Parameters Estimation of Equations of Chemical Kinetics and Mathematical Biology in the Case of Incomplete Experimental Data.

This paper is devoted to a general approach to the parameters estimation of dynamical systems in the case of incomplete experimental data. We analyze a particular case of linear dependence of reduced equation on a group of unknown coefficients which is especially important for different applications. Considered are two typical examples of chemical kinetics equations: the Lotka-Volterra system and canonical reaction of the enzyme synthesis. The methodology of parameters estimation discussed in this paper is based on the solution of overdetermined system using one of minimization method (for example the least squares method). It should be noted that for determination of the unknown parameters we use the reduced equations but not their solutions which in many cases do not exist in the closed form. All the discussed theoretical methods are illustrated with numerical examples which facilitate their practical application. [ABSTRACT FROM AUTHOR]