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Mathematical Research at the University of Cambridge

 

Surface wildfires are generally believed to be the cause of so-called Zombie fires observed in peatlands, that disappear from the surface, smoulder underground during the winter, and “come back to life"" in the spring. Here, we propose that rate-induced tipping (R-tipping) to a subsurface hot metastable state in bioactive peat soils, due to rapid atmospheric warming, is a main cause of zombie fires. Our hypothesis is based on a conceptual soil-carbon model subjected to realistic changes in weather and climate patterns, including global warming scenarios and summer heatwaves.
Mathematically speaking, R-tipping to the hot metastable state is a nonautonomous instability, due to crossing an elusive quasithreshold, in a multiple timescale dynamical system. To explain this instability, we provide a framework that combines a special compactification technique with concepts from geometric singular perturbation theory. This framework allows us to reduce an R-tipping problem due to crossing a quasithreshold to an `exotic' heteroclinic orbit problem in a singular limit. Thus, we identify generic cases of such R-tipping via: (i) unfolding of a codimension-two heteroclinic folded saddle-node type-I singularity for global warming, and (ii) analysis of a codimension-one saddle-to-saddle hetroclinic orbit for summer heatwaves. More generally, these results reveal new types of excitability quasithresholds.

Further information

Time:

06Aug
Aug 6th 2026
09:30 to 10:25

Venue:

Seminar Room 2, Newton Institute

Series:

Isaac Newton Institute Seminar Series