Dynamics in the production of superheavy nuclei in low-energy heavy-ion collisions

We present a review of the recent progress of theoretical models on the description of the formation of superheavy nuclei in collisions of heavy systems. Two sorts of reactions that are the fusion-evaporation mechanism and the massive damped collisions to produce superheavy nuclei are discussed. Problems and further improvements of the capture of colliding partners, the formation of compound nucleus and the de-excitation process are pointed out. Possible combinations in the synthesis of the gap of the cold fusion and $^{48}$Ca induced reactions are proposed by the calculations based on the dinuclear system model and also compared with other approaches. The synthesis of neutron-rich heavy isotopes near sub-shell closure N=162 via transfer reactions in the damped collisions of two actinides and the influence of shell closure on the production of heavy isotopes are investigated. Prospective possibility to reach superheavy nuclei near N=184 via neutron-rich radioactive beams of high intensity in the future is discussed.