|Sebastian Wieczorek (Exeter)||Rate-induced bifurcations: critical rates, non-obvious thresholds, and adaptation failure|
Scientists often find rate-induced bifurcations counter-intuitive because there is no obvious
loss of stability. Mathematically, rate-induced bifurcations cannot in general be described by
classical bifurcation theory or asymptotic approaches. Thus, they require an alternative
approach. I will present an approach based on geometrical singular perturbation theory to study
critical rates of change and (non-obvious) thresholds in terms of connecting (heteroclinic)
orbits and folded singularities. The mathematical approach will be illustrated using examples of
the "critical rate hypothesis" in herbivore-plant interaction and the "compost-bomb instability"
in climate-carbon cycle. I will also discuss repercussions for climate change policy making
which currently focuses on critical levels of the atmospheric temperature whereas the critical
factor may be the rate of warming rather than the temperature itself.