| Abstract: |
| We characterise the range of possible dynamical behaviours for scalar concave and
d-concave nonautonomous differential equations, and demonstrate that nonautonomous saddle-node bifurcations provide a universal mechanism underlying certain critical transitions known as rate-induced tipping. Furthermore, we establish that finite-time Lyapunov exponents serve as reliable and rigorous early warning indicators of such transitions in these systems, as a change in sign occurs prior to the onset of a nonautonomous saddle-node bifurcation. |
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