delay

Topic. The paper is devoted to the study of mutual synchronization of two gyrotrons coupled with delay. As a rule, a theoretical study of synchronization of gyrotrons and other microwave oscillators is usually carried out by numerical simulations using certain well-established models of microwave electronics. Using this approach, it is difficult to provide a fairly complete synchronization pattern, using methods and ideas of nonlinear dynamics.

We study local dynamics of difference and singular perturbed difference-differential systems in the neighborhood of zero equilibrium state. All critical cases in this problem have infinite dimension. We construct special nonlinear equations that play the role of normal form. Their nonlocal dynamics describes the behavior of solution of initial system.