The synchronization of oscillators which interact via a medium (Q1108093)

A system of N nonlinear oscillators which influence one another only as a result of their action on a common medium, is considered. The stability of the synchronized or partially synchronized periodic oscillations in the system is discussed. Special attention is paid to the case when \(N\gg 1\). The problem of the synchronization of such oscillators, which do not interact directly but only indirectly via a common medium, is not new. It is usually assumed that the interaction is weak, so that the oscillators only slightly change their frequency and shape. The term ``synchronization'' usually means one of two effects: 1) the establishment of identical oscillations (in shape and phase) in a system of identical oscillators, 2) the establishment of a common period of oscillation in a system of identical or structurally similar oscillators.