Splay states in globally coupled Josephson arrays: Analytical prediction of Floquet multipliers

Abstract

In recent numerical experiments on series arrays of overdamped Josephson junctions, Nichols and Wiesenfeld [Phys. Rev. A 45, 8430 (1992)] discovered that the periodic states known as splay states are neutrally stable in all but four directions in phase space. We present a theory that accounts for this enormous degree of neutral stability. The theory also predicts the four non-neutral Floquet multipliers to within 0.1% of their numerically computed values. The analytical approach used here may be appli- cable to other globally coupled systems of oscillators, such as multimode lasers, electronic oscillator circuits, and solid-state laser arrays.