Dynamical Analysis of a Tourism-Based Economy

In this paper we investigate the dynamics of a non linear forced oscillator describing a tourism-based economy. We consider a single market, where buyers and sellers adapt their behavior not only to current prices but also to the underlying trend in prices. In this model, the principal part of the demand curve is nonlinearly oscillating with respect to the prices while the principal part of the supply curve is a classic linear increasing function to the price. Assuming equilibrium, we obtain an expression combining demand and supply in the form of a second order non linear differential equation, where both the rate of price change and the rate of change of inflation are taken into account. By interpreting this second order differential equation as a well known pendulum equation, we investigate how the dynamics of the model depend on the parameters. Both stable periodic and chaotic price behavior can occur when the coefficient of forcing term is varied.