Application of a New Method of Nonlinear Dynamical System Identification to Biochemical Problems

A. V. Karnaukhov^* and E. V. Karnaukhova

Institute of Cell Biophysics, Russian Academy of Sciences, Institutskaya ul. 3, Pushchino, Moscow Region, 142290 Russia; E-mail: akarn@icb.psn.ru

^* To whom correspondence should be addressed.

Received July 26, 2002; Revision received November 22, 2002

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The system identification method for a variety of nonlinear dynamic models is elaborated. The problem of identification of an original nonlinear model presented as a system of ordinary differential equations in the Cauchy explicit form with a polynomial right part reduces to the solution of the system of linear equations for the constants of the dynamical model. In other words, to construct an integral model of the complex system (phenomenon), it is enough to collect some data array characterizing the time-course of dynamical parameters of the system. Collection of such a data array has always been a problem. However difficulties emerging are, as a rule, not principal and may be overcome almost without exception. The potentialities of the method under discussion are demonstrated by the example of the test problem of multiparametric nonlinear oscillator identification. The identification method proposed may be applied to the study of different biological systems and in particular the enzyme kinetics of complex biochemical reactions.

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KEY WORDS: identification method, nonlinear dynamical model, enzyme kinetics, biochemical reaction cascade, ordinary differential equation system in Cauchy explicit form, graphic method, Prony's method, asymptotic method

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