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On forced oscillations in groups of interacting nonlinear systems. (English) Zbl 1353.70050
Summary: 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.

70K40 Forced motions for nonlinear problems in mechanics
70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
34C25 Periodic solutions to ordinary differential equations
37K60 Lattice dynamics; integrable lattice equations
70F40 Problems involving a system of particles with friction
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