  A geometric approach is introduced for understanding the phenomenon of phase
synchronization in coupled nonlinear systems in the presence of additive noise.
We show that the emergence of cooperative behaviour through a change of
stability via a Hopf bifurcation entails the spontaneous appearance of a gauge
structure in the system, arising from the evolution of the slow dynamics, but
induced by the fast variables. The conditions for the oscillators to be
synchronised in phase are obtained. The role of weak noise appears to be to
drive the system towards a more synchronized behaviour. Our analysis provides a
framework to explain recent experimental observations on noise-induced phase
synchronization in coupled nonlinear systems.
