Speaker
Description
Power-law dynamical systems are widely used as models in chemistry and biology (e.g., in ecology and epidemiology), as well as in economics and engineering. We study positive solutions to parametrized systems of generalized polynomial equations (with real exponents) in abstract terms. In particular, we identify the relevant geometric objects: the coefficient polytope, the monomial difference, and the monomial dependency subspaces.
Using only linear algebra and polyhedral geometry, we rewrite these polynomial equations and inequalities in terms of binomial equations. The resulting solution sets are then studied using analytical methods; for example, we characterize unique existence for all parameters using Hadamard’s theorem. Furthermore, we revisit mass-action systems that are decomposable and essentially univariate, providing an extension of the classical deficiency one theorem.
