Periodic solutions and global indeterminacy in a model of sustainable tourism

The impact of tourism on economic growth and environmental degradation is one of the most relevant debated issues. Despite the huge strand of empirical literature on the topic, a formalized theoretical investigation of the link between tourism and sustainable economic growth is unfortunately still lacking. To this end, and in line with the literature on the tourist life-cycle hypothesis, we present an endogenous growth model to study the impact of tourism activities and natural resource use on the long run steady state. The aim is to use the principles of bifurcation theory to gain hints on the global properties of the equilibrium, and show the existence of irregular patterns, either indeterminate or chaotic, which possibly suggest the emergence of a (low growth) poverty-environment trapping region.