We carry out an in-depth analysis of the possible dynamical scenarios for scalar differential equations of the type x' = −x²+ q(t)x + p(t), where q : R → R and p : R → R are bounded and uniformly continuous. Particularly, the study of nonautonomous bifurcations of saddle-node type is fundamental to explain the absence or occurrence of rate-induced tipping for the differential equation y'= (y − 2/π arctan(ct))² + p(t) as the rate c varies in [0, ∞). A classical attractor-repeller pair, whose existence for c = 0 is assumed, may persist for any c > 0, or disappear at a certain critical rate c = c_0, giving rise to rate-induced tipping. A suitable example demonstrates that it is possible to have an alternation between intervals of values of c in [0, ∞) where the attractor-repeller pair exists and intervals where it does not.

This is a joint work with

Carmen Nunez, University of Valladolid, Spain, Este endereço de email está sendo protegido de spambots. Você precisa do JavaScript ativado para vê-lo.

Rafael Obaya, University of Valladolid, Spain, Este endereço de email está sendo protegido de spambots. Você precisa do JavaScript ativado para vê-lo.

Martin Rasmussen, Imperial College London, UK, Este endereço de email está sendo protegido de spambots. Você precisa do JavaScript ativado para vê-lo.