Stability and Sustainability of Resource Consumption Networks

Abstract

In this paper, we examine both stability and sustainability of a network-based model of natural resource consumption. Stability is studied from a dynamical systems perspective, though we argue that sustainability is a fundamentally different notion from stability in social-ecological systems. Accordingly, we also present a criterion for sustainability that is guided by the existing literature on sustainable development. Assuming a generic social network of consuming agents' interactions, we derive sufficient conditions for both the stability and sustainability of the model as constraints on the network structure itself. We complement these analytical results with numerical simulations and discuss the implications of our findings for policy-making for sustainable resource governance. I. INTRODUCTION Sustainability of social-ecological systems has been a subject of considerable interest for some time [1]. However, despite its importance, sustainability of this kind is still far from being adequately defined in a rigorous context. The confusion stems directly from the definition of sustainable development itself, given by the Brundtland Commision of the World Commission on Environment and Development (WCED) [2], which leaves much room for interpretation. This has led to a string of research spanning across multiple disciplines in search of a formal definition of the concept [3], [4], [5].From a dynamical systems perspective, sustainability has often been linked to developments in [6], [7], and sometimes even used interchangeably with stability in social-ecological systems [8]. We argue that while stability is indeed relevant in this setting, it is a purely dynamical systems property that does not appropriately account for the ecological nature of the system. Thus a separate formulation of sustainability is needed. This need is underscored by the rising interest of the controls community not only in social-ecological systems, but also in other systems lying at the interface of technological, ecological, and social sciences. Such systems are collectively termed "cyber-physical social systems" [9].