Analysis of Break Points

As another independent topic on direct bifurcation, this chapter deals with the break point, which denotes the value of the transportation cost at the onset of breaking uniformity through bifurcation. It occurs in symmetric spatial platforms, such as the racetrack economy and square and hexagonal lattices. Analytical formulas for this point are derived using replicator and logit dynamics and an analytically solvable economic geography model by Forslid and Ottaviano (J Econ Geogr 3:229–240, 2003). The formulas for the racetrack economy and the square lattice are synthesized. The formulas for a hexagonal lattice are advanced independently. We employ these formulas in describing numerical agglomeration behaviors for the lattices. Chapters 3 , 4 , and 5 are foundations for the bifurcation of the spatial platforms. This chapter covers only direct bifurcation, whereas Chap. 12 will study the break points of secondary and further bifurcations.