Populations of uncoupled limit-cycle oscillators receiving common random
impulses show various types of phase-coherent states, which are characterized
by the distribution of phase differences between pairs of oscillators. We
develop a theory to predict the stationary distribution of pairwise phase
difference from the phase response curve, which quantitatively encapsulates the
oscillator dynamics, via averaging of the Frobenius-Perron equation describing
the impulse-driven oscillators. The validity of our theory is confirmed by
direct numerical simulations using the FitzHugh-Nagumo neural oscillator
receiving common Poisson impulses as an example