A numerical study of the delay in the excitation of oscillations of a magnetostrictive transducer in the frequency multiplication mode based on the model of coupled oscillators is presented. The non-stationary nature of the oscillations excited after the amplitude jump is revealed. The phenomenon is interpreted on the basis of the dynamic potential model. A numerical study of the development of oscillations in time has been carried out, and phase portraits of oscillations have been constructed. The fractal-like nature of nonstationary oscillations is established, which manifests itself in the preservation of the degree of their chaoticity with a change in the value of the calculation step in time.