Svicobians of the compartment models and DaD-stability of the Svicobians: aggregating `0-dimensionalʹ models of global biogeochemical cycles

A Svicobian is the Jacobi matrix for a wider-than-linear class of dynamic models behind a given `stores-flowsʹ diagram. Its particular form can be calculated immediately from the (flow-balanced) diagram to serve the target of standard equilibrium stability analysis. Its general form generates a new concept of matrix stability, the so-called DaD-stability, which is independent of quantitative estimates of stores and flows but is determined by the diagram pattern alone. DaD-stability is proved to be verifiable by the graph theory methods developed earlier to analyse qualitative stability in community matrices. DaD-stability thus appears to be a characteristics of the generic compartment scheme rather than a mere property of a particular dynamic model behind it. Two 8-and 9-compartment schemes of the global carbon cycle published elsewhere have been analysed in terms of DaD-stability in their Svicobians. While the original schemes do not meet the sufficient condition of DaD-stability, the most versions of their further aggregation are found to be DaD-stable, thus providing for comparability among the models.