MS#167. The Dynamics of Synchronization and Phase Regulation, 2023 Subjects: Dynamics 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 coupled oscillators. We present a profusely illustrated review of the geometric theory of the synchronization of periodic attractors, such as biological oscillators, by periodic forcing. Written October, 2023. [PDF] 14 pages, 516 KB Last revised by Ralph Abraham