### 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.

Original language | English |
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Pages (from-to) | 223-232 |

Number of pages | 10 |

Journal | Journal of Computational Methods in Sciences and Engineering |

Volume | 3 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jan 2003 |

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### Scopus subject areas

- Engineering(all)
- Computer Science Applications
- Computational Mathematics

### Cite this

*Journal of Computational Methods in Sciences and Engineering*,

*3*(2), 223-232. https://doi.org/10.3233/JCM-2003-3203

}

*Journal of Computational Methods in Sciences and Engineering*, vol. 3, no. 2, pp. 223-232. https://doi.org/10.3233/JCM-2003-3203

**Parameter Identification For Oscillating Chemical Reactions Modelled By Systems Of Ordinary Differential Equations.** / Babadzanjanz, L. K.; Boyle, J. A.; Sarkissian, D. R.; Zhu, J.

Research output

TY - JOUR

T1 - Parameter Identification For Oscillating Chemical Reactions Modelled By Systems Of Ordinary Differential Equations

AU - Babadzanjanz, L. K.

AU - Boyle, J. A.

AU - Sarkissian, D. R.

AU - Zhu, J.

PY - 2003/1/1

Y1 - 2003/1/1

N2 - 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.

AB - 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.

KW - gradient equations

KW - Lotka-Volterra equtions

KW - minimization

KW - Parameter identification

KW - system of ODEs

UR - http://www.scopus.com/inward/record.url?scp=84948697397&partnerID=8YFLogxK

U2 - 10.3233/JCM-2003-3203

DO - 10.3233/JCM-2003-3203

M3 - Article

AN - SCOPUS:84948697397

VL - 3

SP - 223

EP - 232

JO - Journal of Computational Methods in Sciences and Engineering

JF - Journal of Computational Methods in Sciences and Engineering

SN - 1472-7978

IS - 2

ER -