title: Amplitude-Modulated Bursting: A Novel Class of Bursting Rhythms.
abstract: We report on the discovery of a novel class of bursting rhythms, called amplitude-modulated bursting (AMB), in a model for intracellular calcium dynamics. We find that these rhythms are robust and exist on open parameter sets. We develop a new mathematical framework with broad applicability to detect, classify, and rigorously analyze AMB. Here we illustrate this framework in the context of AMB in a model of intracellular calcium dynamics. In the process, we discover a novel family of singularities, called toral folded singularities, which are the organizing centers for the amplitude modulation and exist generically in slow-fast systems with two or more slow variables.
authors.affiliation: Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Theodore
authors.initials: T
authors.lastname: Vo
authors.affiliation: Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Mark A
authors.initials: MA
authors.lastname: Kramer
authors.affiliation: Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Tasso J
authors.initials: TJ
authors.lastname: Kaper