Loss of Engineering Integrity due to the Erosion of Absolute and Transient Basin Boundaries

This paper explores the engineering relevance of the homoclinic tangling, and associated fractal basins, that are a feature of damped oscillators driven out of a potential well by periodic excitation. For optimal escape under forcing at just below the linear natural frequency, the homoclinic tangency is shown to precipitate a sharp erosion of the safe phase-space basin. This offers a new safety criterion, based on transient motions, that might be extremely valuable in ship capsize. Fractal boundaries in control space arise when an ambient system is suddenly subjected to a pulse of excitation, and their relevance to earthquake studies is briefly discussed.