A Nonlinear ODE Model for a Consumeristic Society

In this paper, we introduce an ODE system to model the interaction between natural resources and human exploitation in a rich consumeristic society. In this model, the rate of change in population depends on wealth per capita, and the rate of consumption has a quadratic growth with respect to population and wealth. We distinguish between renewable and non-renewable resources, and we introduce a replenishment term for non-renewable resources. We first obtain some information on the asymptotic behavior of wealth and population, then we compute all system equilibria and study their stability when the resource exploitation parameter is low. Some numerical simulations confirm the theoretical results and suggest directions for future research.