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/root is an element of for is an element of)>0 to exp{(1/D)/is an element of/(3/2)} for is an element of <0 as <is an element of> passes the bifurcation point (is an element of =0). The results explain why two coupled Rossler oscillators exhibit deformation of the scaling relation of the synchronous length in the nearly synchronous regime.