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Excitability in ramped systems: the compost-bomb instability. (English) Zbl 1219.86006

Summary: 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.

MSC:

86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics
34C26 Relaxation oscillations for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34D15 Singular perturbations of ordinary differential equations
37Gxx Local and nonlocal bifurcation theory for dynamical systems
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
37N25 Dynamical systems in biology
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