In this paper, we propose a bifurcation control method in order to stabilize the trivial steady state in the frequency response of the nonlinear parametric system of ships and try to eliminate jump in the force response, by employing a combined linear-plus-nonlinear feedback control. By theoretically analyzing the modified modulation equations, we show that the unstable region of the trivial steady state of the ship’s parametric rolling motion in longitudinal waves can be shifted and the nonlinear character can be changed, by means of the bifurcation control with the feedback controller. The shift of the unstable region permits the stabilization of the trivial steady state in the frequency response, and the suppression of the discontinuous bifurcation due to the change of the nonlinear character allows the elimination of the jump in the quasistationary force response. By performing numerical simulations, and by comparing the responses of the uncontrolled system and the controlled one, we clarify that the proposed bifurcation control is available for improvement the safety of the ship’s parametric excitation in longitudinal waves.

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