ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


automodulated oscillations

Synchronization of beats in phase-locked loops

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. The observed model has a great variety of dynamical modes both regular and chaotic.