title: Algorithmic global criteria for excluding oscillations.
abstract: We investigate algorithmic methods to tackle the following problem: Given a system of parametric ordinary differential equations built by a biological model, does there exist ranges of values for the model parameters and variables which are both meaningful from a biological point of view and where oscillating trajectories, can be found? We show that in the common case of polynomial vector fields known criteria excluding the existence of non-constant limit cycles lead to quantifier elimination problems over the reals.We apply these criteria to various models that have been previously investigated in the context of algebraic biology.
authors.affiliation: Institut für Informatik II, Universität Bonn, Germany. weber@cs.uni-bonn.de
authors.forename: Andreas
authors.initials: A
authors.lastname: Weber
authors.forename: Thomas
authors.initials: T
authors.lastname: Sturm
authors.forename: Essam O
authors.initials: EO
authors.lastname: Abdel-Rahman
mesh_terms: D000465:Algorithms; D015496:CD4-Positive T-Lymphocytes / Q000821:virology; D053263:Gene Regulatory Networks / Q000502:physiology; D015658:HIV Infections / Q000821:virology; D015497:HIV-1; D008954:Models, Biological; D010507:Periodicity; D011157:Population Dynamics