Abstract. History has proved that the progressive movement of any economic system is not linearly. The periods of intensive growth are replaced by deep crisis phenomena. It was the severe global crises of the XXI century that forced us once again to pay attention to the subject of cyclicality and to consider the specificity of this issue in various industries, in particular – on the example of the sphere of tourism. In modern science, especially in the economy, there are different theoretical justifications of cyclosis, the systems of cycles are proposed depending on the temporary length. There is a hypothesis about the interaction of cycles with each other. Of particular interest is the consideration of the spatio-temporal manifestations of cyclic vibrations. In tourism, there are a number of approaches to the allocation of groups of countries. So at the moment, the United Nations World Tourism Organization (UNWTO) divides the countries of the world into 5 macro-regions. Also widely known in world tourism studies are the center-periphery structure in which the center can be distinguished (economically highly developed countries with a mature international tourism system and integrated tourist specialization), a semi-periphery (medium-developed, often relatively new on the country's tourist map with intensively forming with the support of the state The polyfunctional system of international tourism) and the periphery (economically backward countries with an underdeveloped international tourism market, the enclave nature of development and mainly natural-oriented types of international tourism). The purpose of this work is to investigate the mathematically sound manifestations of cyclicity in the field of tourism on the example of a number of countries of the world, as well as establish possible patterns that manifest in the development cycles of the distinguished groups of regions. To conduct empirical studies, as well as to increase the objectivity of the diagnosis of cyclic vibrations, it is proposed to use a modern mathematical apparatus. In this work, autocorrelation analysis and spectral (Fourier) analysis were used.
Abstract. History has proved that the progressive movement of any economic system is not linearly. The periods of intensive growth are replaced by deep crisis phenomena. It was the severe global crises of the XXI century that forced us once again to pay attention to the subject of cyclicality and to consider the specificity of this issue in various industries, in particular – on the example of the sphere of tourism. In modern science, especially in the economy, there are different theoretical justifications of cyclosis, the systems of cycles are proposed depending on the temporary length. There is a hypothesis about the interaction of cycles with each other. Of particular interest is the consideration of the spatio-temporal manifestations of cyclic vibrations. In tourism, there are a number of approaches to the allocation of groups of countries. So at the moment, the United Nations World Tourism Organization (UNWTO) divides the countries of the world into 5 macro-regions. Also widely known in world tourism studies are the center-periphery structure in which the center can be distinguished (economically highly developed countries with a mature international tourism system and integrated tourist specialization), a semi-periphery (medium-developed, often relatively new on the country's tourist map with intensively forming with the support of the state The polyfunctional system of international tourism) and the periphery (economically backward countries with an underdeveloped international tourism market, the enclave nature of development and mainly natural-oriented types of international tourism). The purpose of this work is to investigate the mathematically sound manifestations of cyclicity in the field of tourism on the example of a number of countries of the world, as well as establish possible patterns that manifest in the development cycles of the distinguished groups of regions. To conduct empirical studies, as well as to increase the objectivity of the diagnosis of cyclic vibrations, it is proposed to use a modern mathematical apparatus. In this work, autocorrelation analysis and spectral (Fourier) analysis were used.