Poverty trap and global indeterminacy in a growth model with open-access natural resources

In this paper we use global analysis techniques to analyze an economic growth model with environmental negative externalities, giving rise to a three-dimensional dynamic system (the framework is the one introduced by Wirl (1997) [53]). The dynamics of our model admits a locally attracting stationary state, which is, in fact, a poverty trap , coexisting with another stationary state possessing saddle-point stability. Global dynamical analysis shows that, under some conditions on the parameters, there exists a continuum of equilibrium trajectories approaching the attractor and one trajectory approaching the saddle point. Therefore, our model exhibits global indeterminacy.