Dynamics of resource production and utilisation in two-component biosphere-human and terrestrial carbon systems

Abstract. This paper analyses simple models for "production-utilisation" systems, reduced to two state variables for producers and utilisers, respectively. Two modes are distinguished: in "harvester" systems the resource utilisation involves active seeking on the part of the utilisers, while in "processor" systems, utilisers function as passive material processors. An idealised model of biosphere-human interactions provides an example of a harvester system, and a model of plant and soil carbon dynamics exemplifies a processor system. The biosphere-human interaction model exhibits a number of features in accord with experience, including a tendency towards oscillatory behaviour which in some circumstances results in limit cycles. The plant-soil carbon model is used to study the effect of random forcing of production (for example by weather and climate fluctuations), showing that with appropriate parameter choices the model can flip between active-biosphere and dormant-biosphere equilibria under the influence of random forcing. This externally-driven transition between locally stable states is fundamentally different from Lorenzian chaos. A behavioural difference between two-component processor and harvester systems is that harvester systems have a capacity for oscillatory behaviour while processor systems do not.