Global–Local Spatial Network

This chapter develops a global–local spatial platform to represent the hierarchical structure of cities, towns, villages, and so on. A global system describes the geographical distribution of a system of cities, whereas each local square lattice models the population size and local geography of each city. Through group-theoretic bifurcation analysis, we elucidate the bifurcation mechanism of the monocentric distribution on a square lattice using the replicator dynamics. This bifurcation explains how satellite places appear around a large city. As a realistic example, we utilize an air network of cities with the seven largest hub airports in the USA. We model this network as a series of local square lattices of various sizes connected by an equidistant economy of a global network. This system simulates the competition among local square lattices. As an example of this competition, we observe successive sustaining bifurcations leading to the gradual emergence of satellite places around a large city in the analysis of an economic geography model. Chapter 9 is a prerequisite for sustaining bifurcations.