Applied Problems of Nonlinear Oscillation and Wave Theory

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.

Time-delayed systems, including coupled ones, became popular models of different physical and biological objects. Often One or few variables of such models cannot be directly measured, these variables are called hidden variables. However, reconstruction of models from experimental signals in presence of hidden variables can be very suitable for model verification and indirect measurement.

A modification of the Newton’s power series method for solving nonlinear ordinary equa-