SYMMETRY-BREAKING BIFURCATION OF A CORE-PERIPHERY MODEL OF MANY CITIES: GROUP-THEORETIC APPROACH

Abstract

The core-periphery model that expresses the city accumulation phenomenon in association with the change of transportation cost has multiple equilibriums for two or three cities. However, there is scarce knowledge on the pattern of spatial accumulation and decentralization of the population when the number of cities is increased further. In this research, the numerical analysis based on computational bifurcation theory and group-theoretic bifurcation theory is carried out on the Core-Periphery model for many cities with the same population that are located symmetrically along a circle. As a result, complex bifurcation behavior of the model has successfully been traced and the accumulation phenomenon of the city has been shown to be engendered via a phased loss of symmetry and spatial period-doubling bifurcation.