Parameter Identification For Oscillating Chemical Reactions Modelled By Systems Of Ordinary Differential Equations

Article type: Research Article

Authors: Babadzanjanz, L.K.^{a; 1} | Boyle, J.A.^{b; 2} | Sarkissian, D.R.^{c; 3} | Zhu, J.^{d; 4}

Affiliations: [a] Department of Applied Mathematics and Processes of Management, St. Petersburg State University, Russia | [b] Department of Biochemistry and Molecular Biology, Mississippi State University, MS, 39762, USA | [c] Department of Mathematics and Statistics, Mississippi State University, MS, 39762, USA | [d] Department of Theoretical and Applied Mathematics, University of Akron, Akron, OH 44325, USA

Correspondence: [4] Corresponding author. E-mail: jzhu@math.uakron.edu. Tel: 01-330-972-8020, Fax: 01-330-374-8630.

Note: [1] E-mail: Levon.Babadzanjanz@pobox.spbu.ru.

Note: [2] E-mail: jab@ra.msstate.edu.

Note: [3] E-mail: sarkiss@math.msstate.edu.

Abstract: The Cauchy problem (also called the initial value problem) for systems of ordinary differential equations with right-hand sides depending on some unknown parameters is considered here. The noisy measurements of one of the variables at the given time moments are assumed to be known. A new algorithm for recovering (identifying) the model parameters is proposed in this paper. The algorithm is based on numerical integration of the gradient equations of a weighted least-squares functional. The right-hand sides of the gradient equations are obtained by numerical integration of the Cauchy problem for the original equations and the Cauchy problem for their partial derivatives with respect to unknown parameters. Numerical experiments for the well-known Lotka-Volterra model of oscillating chemical reactions demonstrate the robustness of the proposed algorithm when the measurements are corrupted by random multiplicative noise. All computations are performed using MATLAB® version 6.0.

Keywords: Parameter identification, system of ODEs, Lotka-Volterra equtions, minimization, gradient equations

Keywords: 65N06, 65N22

DOI: 10.3233/JCM-2003-3203

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 3, no. 2, pp. 223-232, 2003