2020/11/08 by Christian Kuehn, Kuehn, Christian, Iacopo P. Longo +1 · 1 citation
Computer Science · Engineering · Environmental Science · #Dynamical Systems (math.DS) #Ecosystem dynamics and resilience #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2011.04031
openalex publication_date 2020/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper deals with the study of rate-induced tipping in asymptotically autonomous scalar ordinary differential equations. We prove that, in such a tipping scenario, a solution which limits at a hyperbolic stable equilibrium of the past limit-problem loses uniform asymptotic stability and coincides with a solution which limits at a hyperbolic unstable equilibrium of the future limit-problem. We use asymptotic series to approximate such pairs of solutions and characterize the occurrence of a rate-induced tipping by using only solutions calculable on finite time intervals. Moreover, we show that a Melnikov-inspired method employing the asymptotic series allows to asymptotically approximate the tipping point.