(A) PDF for the phase difference of two type1 phase oscillators in the presence of noise for three levels of frequency mismatch. Theoretical predictions (solid lines) are in accordance with numerical results shown as histograms. Dash lines show the phase-locked states in the absence of noise. (B) Cross-Correlogram for two levels of current mismatch for LIF neuron model. Inset: the magnitude of maximum correlation for two neurons shows the positive effect of mismatch in enhancement of correlation.