MS#111. The Dynamics of Synchronization and Phase Regulation, 2003 With Alan Garfinkel Subjects: Dynamics Written: March 3, 2003 Abstract: This is a joint project begun in 1983 and first reported in (Abraham, 1989). We were inspired by Arthur Winfree and have in mind a number of applications to medical physiology and mathematical biology. The main theme is the role of the geometry of periodic attractors -- the shape of an attractive limit cycle and its isochrons -- in determining the phase synchrony of a network of heterogeneous oscillators (periodic or chaotic). We present a profusely illustrated review of the geometric theory of the synchronization of periodic attractors, such as biological oscillators, by periodic pulsatile forcing. We think of this tutorial as "Winfree 101" but a number of new insights are included. [PDF] 35 pages, 344 KB Last revised by Ralph Abraham