Взаимная синхронизация нескольких слабо связанных близких автоколебательных систем

Abstract

The paper considers the effects of mutual synchronization of an arbitrary number of weakly coupled close self-oscillating systems. The concept of mutual synchronization is given. We describe a method that allows us to obtain conditions for coefficients of initial system guarantying synchronization with any given phase differences. This method is based on the Poincaré small parameter method and the Bogolyubov – Shtokalo substitution. The case of in-phase synchronization is considered in detail. A theorem on the synchronization of several weakly coupled close self-oscillating systems is proved. The computations for particular cases of two and three partial systems are given. A numerical example demonstrating the validity of the results is given.