Collective enhancement of precision in networks of coupled oscillators

We analyze conditions under which the precision of coupled oscillators can be improved by synchronization. The improvement in precision, defined as the inverse of the coefficient of variation of the periods, depends on how noise is added to the system. If the magnitude of noise experienced by an oscillator only depends on the state of that oscillator, then the precision of the group rhythm can be improved to N times the precision of an individual uncoupled oscillator, irrespective of the form of the coupling function. However, if the magnitude of the noise also depends on the state of other oscillators, as might be the case for noise caused by synaptic input to neurons, then synchronization may lead to an additional improvement. This collective enhancement of precision is demonstrated both with a simple phase model and a network of integrate-and-fire neurons.