## PANDA (Patterns, Nonlinear Dynamics and Applications)

## Tuesday 3 June 2014

## Department of Mathematical Sciences

## University of Bath

Clare Perryman (Exeter) |
*Can we adapt to a changing environment? Banded instability thresholds for rate-induced bifurcations* |

**Abstract**:
As the rate of environmental change increases, systems sometimes fail to follow a continuously changing stable state. Such behaviour is exhibited in neural systems, electrical circuits, ecosystems, and the climate.
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.