Dynamics in a environmental model with tourism taxation

The purpose of this work is to analyze the dynamics of a model describing the interaction between tourists (T) and environmental resource (E) in the presence or absence of a tourist tax , used to protect the environmental resource. The model highlights how the introduction of tourist tax complicates the dynamics of the system, thus giving origin a new internal equilibrium that is a saddle point, which the stable manifold separates the basin attraction of the locally attractive internal positive point from the one equilibrium point (K; 0), which is also locally stable. Moreover, starting from a system with beta= 0, which has an unstable internal equilibrium, a suitable combination of tourist tax and defensive expenditures leads to a stabilization the protect system.