On stability of synchronized van der Pol oscillators

Method of quasilinear approximation is applied to evaluate stability of operation of two coupled and synchronized van der Pol oscillators. Using this method, at the first step one obtains the amplitude transient equations (van der Pol equations). Then, using routine linearization of these equations one finds the system of four first order linear differential equations. Calculation of the roots of characteristic equation for this system solves the stability problem. The amplitudes and frequency of synchronized oscillations are found from the nonlinear algebraic equations following also from the amplitude transient equations.