### Abstract

Local sensitivity functions ∂Y_{i}/∂p_{k} of many chemical kinetic models exhibit three types of similarity: (i) Local similarity: ratio λ_{ij} = (∂Y_{i}/∂p_{k})/ (∂Y_{j}/∂p_{k}) is the same for any parameter k. (ii) The scaling relation: ratio λ_{ij} is equal to (dY_{i}/dz). (iii) Global similarity: ratio (∂Y_{j}/dz). (iii) Global similarity: ratio (∂Y_{i}/∂p_{k}) (∂Y_{i}/∂p_{m}) is constant in a range of the independent variable z. It is shown that the existence of low-dimensional slow manifolds in chemical kinetic systems may cause local similarity. The scaling relation is present if the dynamics of the system is controlled by a one-dimensional slow manifold. The rank of the local sensitivity matrix is less than or equal to the dimension of the slow manifold. Global similarity emerges if local similarity is present and the sensitivity differential equations are pseudohomogeneous. Global similarity means that the effect of the simultaneous change of several parameters can be fully compensated for all variables, in a wide range of the independent variable by changing a single parameter. Therefore, the presence of global similarity has far-reaching practical consequences for the "validation" of complex reaction mechanisms, for parameter estimation in chemical kinetic systems, and in the explanation of the robustness of many self-regulating systems.

Original language | English |
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Pages (from-to) | 2216-2238 |

Number of pages | 23 |

Journal | Journal of Physical Chemistry A |

Volume | 107 |

Issue number | 13 |

DOIs | |

Publication status | Published - Apr 3 2003 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Journal of Physical Chemistry A*,

*107*(13), 2216-2238. https://doi.org/10.1021/jp026683h

**Similarity of sensitivity functions of reaction kinetic models.** / Zsély, I.; Zádor, Judit; Turányi, T.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry A*, vol. 107, no. 13, pp. 2216-2238. https://doi.org/10.1021/jp026683h

}

TY - JOUR

T1 - Similarity of sensitivity functions of reaction kinetic models

AU - Zsély, I.

AU - Zádor, Judit

AU - Turányi, T.

PY - 2003/4/3

Y1 - 2003/4/3

N2 - Local sensitivity functions ∂Yi/∂pk of many chemical kinetic models exhibit three types of similarity: (i) Local similarity: ratio λij = (∂Yi/∂pk)/ (∂Yj/∂pk) is the same for any parameter k. (ii) The scaling relation: ratio λij is equal to (dYi/dz). (iii) Global similarity: ratio (∂Yj/dz). (iii) Global similarity: ratio (∂Yi/∂pk) (∂Yi/∂pm) is constant in a range of the independent variable z. It is shown that the existence of low-dimensional slow manifolds in chemical kinetic systems may cause local similarity. The scaling relation is present if the dynamics of the system is controlled by a one-dimensional slow manifold. The rank of the local sensitivity matrix is less than or equal to the dimension of the slow manifold. Global similarity emerges if local similarity is present and the sensitivity differential equations are pseudohomogeneous. Global similarity means that the effect of the simultaneous change of several parameters can be fully compensated for all variables, in a wide range of the independent variable by changing a single parameter. Therefore, the presence of global similarity has far-reaching practical consequences for the "validation" of complex reaction mechanisms, for parameter estimation in chemical kinetic systems, and in the explanation of the robustness of many self-regulating systems.

AB - Local sensitivity functions ∂Yi/∂pk of many chemical kinetic models exhibit three types of similarity: (i) Local similarity: ratio λij = (∂Yi/∂pk)/ (∂Yj/∂pk) is the same for any parameter k. (ii) The scaling relation: ratio λij is equal to (dYi/dz). (iii) Global similarity: ratio (∂Yj/dz). (iii) Global similarity: ratio (∂Yi/∂pk) (∂Yi/∂pm) is constant in a range of the independent variable z. It is shown that the existence of low-dimensional slow manifolds in chemical kinetic systems may cause local similarity. The scaling relation is present if the dynamics of the system is controlled by a one-dimensional slow manifold. The rank of the local sensitivity matrix is less than or equal to the dimension of the slow manifold. Global similarity emerges if local similarity is present and the sensitivity differential equations are pseudohomogeneous. Global similarity means that the effect of the simultaneous change of several parameters can be fully compensated for all variables, in a wide range of the independent variable by changing a single parameter. Therefore, the presence of global similarity has far-reaching practical consequences for the "validation" of complex reaction mechanisms, for parameter estimation in chemical kinetic systems, and in the explanation of the robustness of many self-regulating systems.

UR - http://www.scopus.com/inward/record.url?scp=0038393175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038393175&partnerID=8YFLogxK

U2 - 10.1021/jp026683h

DO - 10.1021/jp026683h

M3 - Article

AN - SCOPUS:0038393175

VL - 107

SP - 2216

EP - 2238

JO - Journal of Physical Chemistry A

JF - Journal of Physical Chemistry A

SN - 1089-5639

IS - 13

ER -