Existence and stability of periodic solutions for chains of connected oscillators - Maistrenko, Yu. L.; Popovich, O. V. (Ukrains’kyi Matematychnyi Zhurnal, 1997)
We consider a nonlinear system of difference equations. This system corresponds to chains of N symmetrically connected oscillators with sufficiently general type of connection, which includes, among others, local and global connection. We prove a theorem on the existence and stability of space-time periodic solutions of such systems for sufficiently small values of the parameter of connection ɛ.