Hidden synchronization of phase-locked loops with nonlinear delay

In this paper, we consider a mathematical model of a phase locked loop system taking into account nonlinearity in the delay in the case of a fractional rational second-order integrating filter. We obtain conditions for the existence of several quasi-synchronous modes of the system, which determine the phase synchronization modes, and analyze the influence of the nonlinear delay on the phase multistability. We develop numerical and analytical conditions for the existence of hidden synchronization of phase systems and construct an algorithm for determining the influence of nonlinear delays on synchronization modes.