Excitability in ramped systems: the compost-bomb instability

Excitability in ramped systems: the compost-bomb instability

http://rspa.royalsocietypublishing.org/content/early/2010/11/24/rspa.2010.0485.full

Proc. R. Soc. A, published online before print November 24, 2010; doi: 10.1098/rspa.2010.0485
The paper studies a novel excitability type where a large excitable response appears when a system’s parameter is varied gradually, or ramped, above some critical rate. This occurs even though there is a (unique) stable quiescent state for any fixed setting of the ramped parameter. We give a necessary and a sufficient condition for the existence of a critical ramping rate in a general class of slow–fast systems with folded slow (critical) manifold. Additionally, we derive an analytical condition for the critical rate by relating the excitability threshold to a canard trajectory through a folded saddle singularity. The general framework is used to explain a potential climate tipping point termed the ‘compost-bomb instability’—an explosive release of soil carbon from peatlands into the atmosphere occurs above some critical rate of global warming even though there is a unique asymptotically stable soil carbon equilibrium for any fixed atmospheric temperature.