Sustainability Analysis of Interconnected Food Production Systems via Theory of Barriers

Abstract: Controlled environment agriculture (CEA) is used for efficient food production. Efficiency can be increased further by interconnecting different CEA systems (e.g. plants and insect larvae or fish and larvae), using products and by-products of one system in the other. These interconnected systems define an overall system that can be described by models of interacting species. It is necessary to identify system parameters (e.g. initial species concentration, harvest rate, feed quality, etc.) such that the resources are not exhausted. For such systems with interacting species, modelled by the Lotka-Volterra equations, a set-based approach based on the recent results of the theory of barriers to exactly determine the so-called admissible set (also known as viability kernel) and the maximal robust positively invariant set is presented. Using an example of a larvae-fish based production system, steps to obtain special trajectories which are the boundaries of the admissible set are shown. This admissible set is used to prevent the under and over population of the species in the CEA. Furthermore, conditions of the system parameters are stated, such that the existence of these trajectories can be guaranteed.