Josephson Junction Arrays: Puzzles and Prospects

Among the best studied many oscillator systems in recent years are Josephson junction arrays. This paper summarizes some theoretical progress likely to be especially useful in the quest to design practical electromagnetic sources at very high frequencies. Outstanding puzzles and future theoretical directions are also described. The central problem is one which is pervasive in the general study of nonlinear oscillators: under what conditions will the various elements oscillate with the same frequency and phase?