Positive Quadratic System Modeling Based on Singular Perturbation

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  • 特異摂動によるポジティブ2次システムモデリング
  • トクイセツドウ ニ ヨル ポジティブ 2ジ システム モデリング

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Abstract

Our previous study proposed a positive quadratic system representation for molecular interaction in a cell, including a signal transduction pathway and a gene regulatory network, and also presented a method for estimating a positive invariant set depending on the initial state. As an extension towards wider applications of this approach, this paper proposes a system representation called here a singularly perturbed positive quadratic system, and shows that every positive rational system, which is used as a mathematical model expressing biological behavior, can be approximately represented by a quasi-steady state system of a singularly perturbed positive quadratic system. In addition, we prove that the singularly perturbed positive quadratic system preserves stability at an equilibrium point of the positive rational system.

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