Safe basins for a nonlinear oscillator with ramped forcing

Abstract

A nonlinear oscillator is studied in the presence of external forcing for which the amplitude initially depends on time. The focus is on the sizes of the basins of attraction which do not lead to unbounded motions, collectively termed the 'safe basin'. Direct comparisons are drawn between the regime of constant forcing amplitude and that where the forcing amplitude initially depends on time. In the process, questions from previous literature are answered and previously unexplained phenomena are understood. Furthermore, we witness a new phenomenon, not previously observed for the system studied.