Abstract

This paper considers the design of networks for sustainability in the context of a socio-ecological model of natural resource consumption. Recent work has developed a notion of sustainability motivated by the ecological modelling literature and a set of conditions on the network structure & system parameters that ensure that this sustainability definition is satisfied. This paper translates these sustainability criteria into an optimization problem that optimizes both a network’s topology and its interaction weights to make the sustainability time horizon as long as possible. This problem treats system stability as a constraint, and it enforces an edge budget for the network, which reflects realistic resource limitations by limiting the number of edges that a network can contain. The introduced optimization problem is then solved analytically for a network of homogeneous agents, and numerical results are shown for heterogeneous agents. Finally the derived optimal network topologies are shown to have varying impacts on the behavior of the resource consumption model. Together, these results suggest that homogeneity in the underlying network structure promotes sustainability in the sense defined herein.

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