title: Thresholds of excitability in three-dimensional dynamical systems.
abstract: A two-dimensional threshold surface of an excitable system is found as a set of threshold trajectories calculated step by step in cross sections of the phase space. The method leads to a highly nonlinear boundary value problem that can be solved numerically with the use of adaptive multiple shooting and continuation methods. We demonstrate this technique by examining a model of a biochemical oscillator with two positive feedbacks. Generalization to arbitrary dimension is discussed.
authors.affiliation: Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Prague Institute of Chemical Technology, Technická 5, 166 28 Prague 6, Czech Republic.
authors.forename: Michal
authors.initials: M
authors.lastname: Voslar
authors.forename: Igor
authors.initials: I
authors.lastname: Schreiber