Characteristic relations of type-I intermittency in the presence of noise

Near the point of tangent bifurcation, the scaling properties of the laminar length of type-I intermittency are investigated in the presence of noise. Based on analytic and numerical studies, we show that the scaling relation of the laminar length is dramatically deformed from 1/sqrt[epsilon] for epsilon>0 to exp(1/D)|epsilon|(3/2) for epsilon<0 as epsilon passes the bifurcation point (epsilon=0). The results explain why two coupled Rossler oscillators exhibit deformation of the scaling relation of the synchronous length in the nearly synchronous regime.