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Abstract:
Reservoir models play an important role in representing fluxes of matter and energy in ecological systems
and are the basis of most models in biogeochemistry.
These models are commonly used to study the effects of
environmental change on the cycling of biogeochemical
elements and to predict potential transitions of ecosystems
to alternative states. To study critical regime changes
of time-dependent, externally forced biogeochemical systems,
we analyze the behavior of reservoir models typical
for element cycling (e.g., terrestrial carbon cycle) with
respect to time-varying signals by applying the mathematical
concept of input to state stability (ISS). In particular,
we discuss ISS as a generalization of preceding stability
notions for non-autonomous, non-linear reservoir models
represented by systems of ordinary differential equations
explicitly dependent on time and a time-varying input signal.
We also show how ISS enhances existing stability
concepts, previously only available for linear time variant (LTV) systems, to a tool applicable also in the non-linear case.
