๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

A Family of Sparse Polynomial Systems Arising in Chemical Reaction Systems

โœ Scribed by Karin Gatermann; Birkett Huber

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
511 KB
Volume
33
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 m is of particular interest. We show that the simplest cases are equivalent to binomial systems and are explained with the help of toric varieties. The argumentation is constructive and suggests algorithms. In general the solution structure is highly determined by the properties of the two graphs. We explain how the graphs determine the Newton polytopes of the system of sparse polynomials and thus determine the solution structure. Results on positive solutions from real algebraic geometry are applied to this particular situation. Examples illustrate the theoretical results.

๐Ÿ“œ SIMILAR VOLUMES

The number of limit cycles for a family
The number of limit cycles for a family of polynomial systems
โœ Guanghui Xiang; Maoan Han; Tonghua Zhang ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 441 KB

In thin paper~ the number of hmlt cycles m a family of polynomial systems was studmd by the bifurcation methods With the help of a computer algebra system (e.g., MAPLE 7 0), we obtain that the least upper bound for the number of hmlt cycles appearing m a global bifurcation of systems (2.1) and ( 2.2

Some Polynomial Systems Associated with
Some Polynomial Systems Associated with a Certain Family of Differential Operators
โœ Kung-Yu Chen; Chuan-Jen Chyan; H.M. Srivastava ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 204 KB

The authors aim at presenting several (presumably new) classes of linear, bilinear, and mixed multilateral generating functions for some general systems of polynomials which are defined by means of a certain family of differential operators. Some of the generating functions considered here are assoc