|Clare Perryman (Exeter)||Can we adapt to a changing environment? Banded instability thresholds for rate-induced bifurcations|
Multiscale systems have critical rates of change at which solutions suddenly fail to adapt to the changing environment. This situation corresponds to a folded singularity appearing. Above the critical rate, there is an instability threshold that separates the initial states that follow the changing stable state, from those that fail to follow and move away.
We uncover a special threshold that arises from a type I folded saddle-node. The threshold has an intriguing banded structure. The structure arises from a combination of the complicated dynamics near a folded node, and the simple threshold behaviour due to a folded saddle.