Dennis Öberg: Analyzing polynomial dynamical systems using algebraic methods

Abstract: The main purpose of the work presented in this master thesis has been to study how algebraic methods can be used for studying polynomialdynamical systems. Algebraic methods for determining the number ofsteady states, finding said states and determining the stability properties of them are presented, as well as methods for reducing the dimension of and for reducing the number of parameters in such systems. It is also illustrated how these methods can be used to study some classes of systems which appear in applications.