Abstract
We discuss a recently proposed model for the sawtooth oscillations of atmospheric carbon observed in ice age cores. The model at its simplest arises from a single reaction involving just two species, oceanic biomass and nutrient, and bears similarity to models which have been proposed to explain oscillations in glycolysis. We show that the sawtooth behaviour, and associated spiking of one of the constituents, is associated with the existence of a conservative nonlinear oscillator with an asymmetric potential at high values of the energy, and we give asymptotic descriptions of the solutions. We extend the analysis to a more complicated model which includes competition between planktonic species.
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