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Sparse polynomial differential systems modelling mass action kinetics

We investigate the model of mass action kinetics describing the dynamical behavior of chemical reactions. The right hand side of the ordinary differential equations is given by sparse polynomials. The structure of the polynomials is given by the chemical reaction (a directed graph) and the stoichiometric coefficients (given by a bipartite graph). Based on the work by Feinberg, Horn, Jackson, Clarke we will present dynamical aspects of steady states from an algebraic point of view. The Liapunov function in Feinberg's deficiency zero theorem exploits the lattice defined by the polynomials. Clarke's concept of stability of a network (of all steady states for all values of the rate constants) is closely related to the concept of of toric varieties from algebraic geometry. Toric varieties are even exploited in the symbolic computation of Hopf bifurcation points. As an example we present the oscillation of calcium in a cell.
Type of Seminar:
Public Seminar
Prof. Dr. Karin Gatermann
DFG, ZIB, FU Berlin
Nov 04, 2002   17:15

ETH-Zentrum, Building ETL, Room K 25, Physikstrasse 3, 8006 Zurich
Contact Person:

Prof. P. Parrilo
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Biographical Sketch:
Born 1961 Bad Oldesloe, Germany / 1986 diploma thesis at Universitaet Hamburg/ 1990 doctor's degree at Universitaet Hamburg/ 1989 - 1995 assistant at Konrad-Zuse-Zentrum Berlin/ 1995 - 2001 C1 at Freie Universitaet Berlin/ 2000 habilitation at Freie Universitaet Berlin/ 2001 - Heisenberg-Stipendium of DFG. The habilitation thesis appeared as volume 1728 of Lecture Notes in Mathematics by Springer with title Computer Algebra methods for equivariant dynamical systems.