Model containing coupled subsystems with oscillations of different types

Abstract

Consideration was given to an autonomous model containing coupled subsystems (MCCS) and, in the absence of couplings between the subsystems, falling down into systems of ordinary differential equations. It is assumed that the subsystems admit different types of nondegenerate single-frequency oscillations. Solved were the problems of oscillations in MCCS, their stability, and stabilization of MCCS oscillation by smooth autonomous coupling controls. It was shown how the developed theory is applied to the coupled Duffing and Van der Pol oscillators.