Finally we came out with the submission of the paper on Petri Nets. This was the topic of various posts collected under the name of reservoirology. You can see the submitted paper by clicking on figure below.
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The paper deals with the graphical representation of lumped-parameter hydrological models or, as we called them, Hydrological Dynamical Systems (HDSys). We were not satisfied with previous representations of such models and we thought that figures in literature do not convey the right information to the readers, usually being not enough explicative. At the same time, we streamlined the process to document appropriately the models for reproducibility. Insufficiently explained HDSys are not reproducible and this is bad for hydrology. Then we setup a one-to-one relationship between graphics and mathematics and this could help the passage from the initial ideas about processes to their representation in formulas. At that point, we asked ourselves if our graphic tools were suitable to represent models with the ambition to explore the interactions between hydrology and ecosystems, and therefore account for their co-evolution. We obtained a positive answer adding a graphical feature to visualize how state variables regulate the models' parameters through quantities called controllers. Once the representation was complete, we could observe the analogy of our representation with those used in other sciences, as, for instance, theoretical biology. This open the way to connect hydrological work to the graphical methods in the non-linear systems theory.
