Resonant escape induced by a finite time harmonic excitation

The purpose of this paper is twofold. First, we obtain the critical forcing needed for a resonant escape in finite time in the presence of damping. Second, we adapt the isolated resonance approximation (AIR) method to find the escaping time and analyze the escape in finite time. Approximations of the escape time on both the phase and the parameter planes were obtained. In particular, a peculiar fractal-like boundary of the finite-time escape region was revealed. This discovery helps to better understand the limitations of AIR and explains the sensitivity of the numerical experiments to the integration time.