Sustainability or societal collapse, dynamics and bifurcations of the handy model

Arnaud Tonnelier (1)

1 TRIPOP - Modélisation, simulation et commande des systèmes dynamiques non lisses

The overexploitation of natural resources by our industrial society questions its longterm sustainability. Recently, a simple nature-society interrelation model, called the HANDY model, has been proposed by Montesharrei et al (2014) to address this concern with a special emphasis on the role of the stratification of the society. In this paper we analyse 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.

Mots clés: Collapse; Sustainability; Human-Nature Model; Bifurcation; Dynamical system

Domaines: Systèmes dynamiques [math.DS]

Arnaud Tonnelier. Sustainability or societal collapse, dynamics and bifurcations of the handy model. SIAM Journal on Applied Dynamical Systems, 2023, 22 (3), ⟨10.1137/22m1494336⟩. ⟨hal-03659720v2⟩