RT info:eu-repo/semantics/article
T1 Rate-induced tipping and saddle-node bifurcation for quadratic differential equations with nonautonomous asymptotic dynamics
A1 Longo, Iacopo Paolo
A1 Núñez Jiménez, María del Carmen
A1 Obaya, Rafael
A1 Rasmussen, Martin
K1 Critical transition
K1 Nonautonomous bifurcation
K1 Nonautonomous dynamical systems
K1 Pullback attractor
K1 Pullback repeller
K1 Rate-induced tipping
K1 Skew product flow
AB An in-depth analysis of nonautonomous bifurcations of saddle-nodetype for  scalar differential equations $x'=-x^2+q(t)\,x+p(t)$,where $q\colon\R\to\R$ and $p\colon\R\to\R$ are bounded and uniformlycontinuous, is fundamental to explain the absence or occurrence ofrate-induced tipping for the differential equation$y' =(y-(2/\pi)\arctan(ct))^2+p(t)$ as the rate $c$ varies on $[0,\infty)$.A classical attractor-repeller pair, whose existence for $c=0$ is assumed,may persist for any $c>0$, or disappear for a certain critical rate $c=c_0$,giving rise to rate-induced tipping. A suitable example demonstrates thatthis tipping phenomenon may be reversible.
YR 2020
FD 2020
LK http://uvadoc.uva.es/handle/10324/40888
UL http://uvadoc.uva.es/handle/10324/40888
LA eng
NO Sometido a publicación
DS UVaDOC
RD 28-nov-2024