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- Karin Gatermann, Markus Eiswirth, Anke Sensse
- J. Symb. Comput.
- 2005

A family of polynomial differential systems describing the behavior of a chemical reaction network with generalized mass action kinetics is investigated. The coefficients and monomials are given by graphs. The aim of this investigation is to clarify the algebraic-discrete aspects of a Hopf bifurcation in these special differential equations. We apply… (More)

We consider a family of sparse polynomial systems denned by a directed graph and a bipartite graph which depend on certain parameters. A convex polyhedral cone serves as a representative of all positive solutions of the family. We study the boundary of this cone with Bernstein’s second theorem and Viro’s method. In particular we present new results about… (More)

- Jan Verschelde, Karin Gatermann, Ronald Cools
- Discrete & Computational Geometry
- 1996

- Karin Gatermann, Birkett Huber
- J. Symb. Comput.
- 2002

The positive steady states of chemical reaction systems modeled by mass action kinetics are investigated. This sparse polynomial system is given by a weighted directed graph and a weighted bipartite graph. In this application the number of real positive solutions within certain affine subspaces of R is of particular interest. We show that the simplest cases… (More)

This paper investigates generic bifurcations from a D m-invariant equilibrium of a D m-symmetric dynamical system, for m = 3 or 4, near points of codimension-2 steady-state mode interactions. The center manifold is isomorphic to IR 3 or IR 4 and is non-irreducible. Depending on the group representation, in the unfolding of the linearization we nd:… (More)

The aim of this paper is to compute all isolated solutions to symmetric polynomial systems. Recently, it has been proved that modelling the sparse structure of the system by its Newton polytopes leads to a computational breakthrough in solving the system. In this paper, it will be shown how the Lifting Algorithm, proposed by Huber and Sturmfels, can be… (More)

- Karin Gatermann, Andreas Hohmann
- IMPACT Comput. Sci. Eng.
- 1991

s of Articles in This Issue

DISSERTATION zur Erlangung des akademischen Grades doctor rerum naturalium Dedicated to the memory of KARIN GATERMANN Table 1: List of mathematical symbols C field of complex numbers R field of real numbers Z ring of integer numbers C[x] ring of polynomials with coefficients in the field of complex numbers I ideal I def, tor deformed toric ideal V (I)… (More)

- Karin Gatermann
- Applicable Algebra in Engineering, Communication…
- 1996

The results from Invariant Theory and the results for semi-invariants and equivariants are summarized in a suitable way for combining with Gröbner basis computation. An algorithm for the determination of fundamental equivariants using projections and a Poincaré series is described. Secondly, an algorithm is given for the representation of an equivariant in… (More)