Munich Personal RePEc Archive

Global bifurcation mechanism and local stability of identical and equidistant regions

Gaspar, José M. and Ikeda, Kiyohiro and Onda, Mikihisa (2019): Global bifurcation mechanism and local stability of identical and equidistant regions.

[img] PDF

Download (687kB)


We provide an analytical description of possible spatial patterns in economic geography models with three identical and equidistant regions by applying results from General Bifurcation mechanisms. We then use Pflüger's (2004, Reg Sci Urb Econ) model to show what spatial patterns can be uncovered analytically. As the freeness of trade increases, a uniform distribution undergoes a direct bifurcation that leads to a state with two identical large regions and one small region. Before this bifurcation, the model encounters a minimum point above which a curve of dual equilibria with two small identical regions and one small region emerges. From further bifurcations, the equilibrium with one large region encounters agglomeration in a single region, while the equilibrium with one small region encounters a state with two evenly populated regions and one empty region. A secondary bifurcation then leads to partial agglomeration with one small region and one large region. We show that an asymmetric equilibrium with populated regions cannot be connected with other types of equilibria. Therefore, an initially asymmetric state will remain so and preserve the ordering between region sizes.

Atom RSS 1.0 RSS 2.0

Contact us: mpra@ub.uni-muenchen.de

This repository has been built using EPrints software.

MPRA is a RePEc service hosted by Logo of the University Library LMU Munich.