Dynamics Of A Globally Coupled Oscillator Array

We study a set of N globally coupled ordinary differential equations of the form encountered in circuit analysis of superconducting Josephson junction arrays. Particular attention is paid to two kinds of simple time-periodic behavior, known as in-phase and splay phase states. Some results valid for general N, as well as further results for N = 2 and N --> infinity, are presented; a recurring theme is the appearance of very weak dynamics near the periodic states. The implications for Josephson junction arrays are discussed.