A method for the investigation of mutually coupled oscillators

A nonlinear differential matrix equation for describing motion in a collection of oscillators coupled by an arbitrary linear multiterminal network is presented. The proposed method, at its initial stage, makes it possible to predict the behavior of the oscillators on the basis of the eigenvalues and eigenvectors of the multiterminal network without solving the system of nonlinear differential equations. Steady amplitudes and phases of the oscillators can be determined easily when only one mode exists. In other cases it is necessary to solve the equations in new variables and to determine possible steady-state regimes.