Adapting to a Changing Environment: Non-obvious Thresholds in   Multi-Scale Systems
  Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these processes with a new nonlinear phenomenon---an intricate threshold where a forced system fails to adiabatically follow a changing stable state. In systems with multiple time-scales such thresholds are generic, but non-obvious, meaning they cannot be captured by traditional stability theory. Rather, the phenomenon can be analysed using concepts from modern singular perturbation theory: folded singularities and canard trajectories, including composite canards. Thus, non-obvious thresholds should explain the failure to adapt to a changing environment in a wide range of multi-scale systems including: tipping points in the climate system, regime shifts in ecosystems, excitability in nerve cells, adaptation failure in regulatory genes, and adiabatic switching in technology. 
Clare Perryman and Sebastian Wieczorek
math.DS nlin.CD