A network landscape model: stability analysis and numerical tests

A Network Landscape Model (NLM) for the evaluation of the ecological trend of an environmental system is here presented and investigated. The model consists in a network of dynamical systems, where each node represents a single Landscape Unit (LU), endowed by a system of ODEs for two variables relevant to the production of bio-energy and to the percentage of green areas, respectively. The main goal of the paper consists in testing the relevance of connectivity between the LUs. For this purpose we consider first the Single LU Model (SLM) and investigate its equilibria and their stability, in terms of two bifurcation parameters. Then the network dynamics is theoretically investigated by means of a bifurcation analysis of a proper simplified differential system, that allows to understand how the coupling between different LUs modifies the asymptotic scenarios for the single LU model. Numerical simulations of NLM are performed, with reference to an environmental system in Northern Italy, and results are discussed in connection with SLM.