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2008•Unpublished venueOpen access

ON THE ROLE OF DIFFERENTIAL ALGEBRA IN BIOLOGICAL MODELING

François Boulier

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Abstract

Differential algebra is an algebraic theory for studying systems of polynomial ordinary differential equations (ODE). Among all the methods developed for system modeling in cellular biology, it is particularly related to the well-established approach based on nonlinear ODE. A sub-theory of the differential algebra, the differential elimination, has proved to be useful in the parameters estimation problem. It seems however still more promising in the quasi-steady state approximation theory, recent results show.

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What this paper is about

Differential algebra is an algebraic theory for studying systems of polynomial ordinary differential equations (ODE). Among all the methods developed for system modeling in cellular biology, it is particularly related to the well-established approach based on nonlinear ODE. A sub-theory of the differential algebra, the differential elimination, has proved to be useful in the parameters estimation problem. It seems however still more promising in the quasi-steady state approximation theory, recent results show.

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Available abstract

Differential algebra is an algebraic theory for studying systems of polynomial ordinary differential equations (ODE). Among all the methods developed for system modeling in cellular biology, it is particularly related to the well-established approach based on nonlinear ODE. A sub-theory of the differential algebra, the differential elimination, has proved to be useful in the parameters estimation problem. It seems however still more promising in the quasi-steady state approximation theory, recent results show.

Key concepts: Differential algebra, Algebraic differential equation, Ode, Differential algebraic geometry, Algebra over a field, Differential (mechanical device), Differential algebraic equation, Ordinary differential equation

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