Abstract:

In empirical studies the application of tourism life cycle theory is questioned because of the different modes of study sites and difficulty in dividing life cycle stages. This study selected 14 national historic site parks in the United States as an example. The four-parameter Logistic model, which is rarely used in tourism research, was combined with the primary function, the quadratic function, the cubic function, and the Gaussian multi-peak analysis methods to fit the life cycle of the tourist destinations. The study found that the four-parameter Logistic model combined with the primary function, the quadratic function, and the cubic function can better fit the life cycle of these tourist destinations; the four-parameter Logistic curve can be used to quantitatively divide the tourism life cycle by the upper bend point, the inflection point, and the lower bend point into initial exploration, development, consolidation, and stagnation stages, and the primary function, the quadratic function, and the cubic function can fit the recession or rejuvenation stage of the tourist destinations, which addresses the concerns of scholars that it is difficult to quantitatively divide the life cycle stages. Based on the development trend after the stagnation period of tourist destinations, the life cycle type of the tourism destinations can be identified. The Gaussian multi-peak analysis method fits the life cycle of the tourism destinations into a volatility Gaussian peak, which retains tourism change to a greater extent. The characteristics of fluctuation in the life cycle of tourist destinations completely answer the questions of scholars about the life cycle model's application in tourism research.

Key words: tourism life cycle, four-parameter Logistic model, Gaussian multi-peak analysis