Rate-induced phenomena in dynamical systems with attracting limit cycles

We study the behavior of dynamical systems under a time-dependent change of an external parameter. We are interested in phenomena induced by the parameter changing sufficiently quickly, and we refer to these as rate-induced phenomena. We investigate such rate-induced phenomena in continuous-time planar dynamical systems, where the underlying fixed-parameter autonomous dynamics have limit cycles attractors, extending the work of Alkhayuon and Ashwin [Chaos 28(3), 033608 (2018)]. We discover new phenomena of rate-induced phase sensitivity, where the rate at which the parameter changes can trigger finite-time unpredictability in the dynamics. We also find that this new phenomenon interacts in an interesting way with the established notion of rate-induced tipping.