A Nonlinear ODE Model for a Consumeristic Society

In this paper we introduce an ODE system to model the interaction between nature 1 resources and human exploitation in a rich consumeristic society. In this model the rate of change of 2 population depends on wealth per capita, and the rate of consumption has a quadratic growth with 3 respect to population and wealth. As in our previous work, we distinguish between renewable and 4 non renewable resources, and we introduce a replenishment term for non renewable resources. We 5 first get some information on the asymptotic behaviour of wealth and population, then we compute 6 all the equilibria of the system and we study their stability when the parameter of exploitation of 7 resources is small. Some numerical simulations confirm the theoretical results, and give suggestions 8 for future research.