The highly nonlinear roll and capsizing motion of ships in random seas are analyzed in this paper by utilizing the Melnikov function and phase space flux. Influence factors on the phase space flux, such as significant wave height, significant wave frequency, nonlinear righting arm and damping characteristic, have taken into consideration. As an example, when a fishing vessel of 30.7 m long and 6.9 m wide is considered to sail in the seas of ISSC wave spectrum, the Melnikov function in time domain is computed. Also, the relation between the phase space flux and the Melnikov function has attained and the influence of significant wave height on the phase space flex has discussed. It is shown that the phase space flux is monotonically increasing as the significant wave height increases, while the safe basin is decreasing rapidly.

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