Dynamical integrity of the safe basins in a problem of forced escape.

This paper explores the use of the approximation of isolated resonance method for determining the safe basins (SBs) in the problem of escape from a potential well. This study introduces a novel approach to capture the location and shape of the SBs and establish their erosion profiles. This research highlights the concept of "true" safe basins, which remain invariant with phase shifts, a critical factor often faced in real-world applications.

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.