биения

Dynamics of two phase-locked loops (PLL) with first order low-pass filters coupled via additional phase discriminator is studied. Mathematical models of the partial systems are pendulum-like type. Thus, mathematical model of the whole system consists of four ordinary differential equations. Phase space of the model is a cylindrical with two cyclic variables. In a case of low-inertial control loops the model transforms into dynamical system with toroidal phase space.

Nonlinear dynamics of the ensemble consisting of three phase­locked generators, which are coupled in a ring, is discovered. By force of computational modeling, which is based on the theory of oscillations, the regimes of the generators collective behavior is examined; the districts of synchronous and quasi­synchronous regimes are distinguished in the parameter space; the restructuring of the dynamics behavior on the boards of the distinguished districts is analyzed.