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We performed modeling of the collision of two spherical nuclei resulting in capture. For this aim the stochastic differential equations are used with the white or colored noise and with the instant or retarding friction, respectively. The dissipative forces are proportional to the squared derivative of the strong nucleus-nucleus interaction potential (SnnP). The SnnP is calculated in the framework of the double folding approach with the density-dependent M3Y NN-forces. Calculations performed for 28Si+144Sm reaction show that accounting for the fluctuations typically reduces the capture cross sections by not more than 10%. In contradistinction, the influence of the memory effects is found resulting in about 20% enhancement of the cross section

Retarding friction versus white noise in the description of heavy ion fusion