(untitled) (Nonlinear Studies, 2011)
A method of analysis of integrate-and-fire models, which consist of pulse-coupled biological oscillators is developed. A thoroughly constructed map and technique of investigation for differential equations with discontinuities at non-fixed moments are in the basis of the analysis. Synchronization and existence of periodic motions of oscillators, which are not quite identical are investigated. The second conjecture of Peskin is proven. Examples with numerical simulations are given to validate the theoretical results. Perspectives are discussed.