On forced oscillations in groups of interacting nonlinear systems

• We study periodically forced motion in groups of interacting systems.
• We present sufficient conditions for the existence of a periodic solution.
• The result is obtained as an application of a topological approach.

Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface, possibly with a boundary, in an external periodic field. We present sufficient conditions for the existence of a periodic solution for the whole system. The result is illustrated by a series of examples including a chain of strongly coupled pendulums in a periodic field.