Dynamical Analysis of a Discrete Time Tourism Model

Following Venturi 2000, we consider a single market as a discrete tourism dynamical system, where buyers and sellers adapt their behavior not only to the current prices but also in their trend in the time. In agreement to empirical data, we study a model involving an unusual shape for the main part of the demand function, which is formalized as an oscillating function. In equilibrium, we obtain a system pendulum type which result in a second order non-linear difference equation. We analyze the dynamic behavior of the trajectories of prices which is strongly affected by variation of the parameters We demonstrate the presence of a chaotic attractor and the occurrence of complex motion in a properly specified price dynamics. The economic implications of this analysis are discussed.