Sustainability or Societal Collapse: Dynamics and Bifurcations of the HANDY Model

The overexploitation of natural resources by our industrial society questions its long-term sustainability. Recently, a simple nature-society interrelation model, called the HANDY (Human And Nature DYnamics) model, has been proposed by Motesharrei, Rivas, and Kalnay [Ecol. Econ., 101 (2014), pp. 90-102] to address this concern with a special emphasis on the role of the stratification of the society. In this paper we analyze the dynamics of this model, and we explore the influence of two parameters: the nature depletion rate and the inequality factor. We characterize the asymptotic states of the system through a bifurcation analysis, and we derive several quantitative predictions. We show that some collapses are irreversible and, depending on the wealth production factor, bistability regimes can be obtained. In particular, a sustainable equilibrium can coexist with cycles of prosperity and collapse. We discuss the possible policies to prevent undesirable fates.