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Bifurcations in Regional Migration Dynamics

Marcus Berliant () and Fan-chin Kung ()

MPRA Paper from University Library of Munich, Germany

Abstract: The tomahawk bifurcation is used by Fujita et al. (1999) in a model with two regions to explain the formation of a core-periphery urban pattern from an initial uniform distribution. Baldwin et al. (2003) show that the tomahawk bifurcation disappears when the two regions have an uneven population of immobile agricultural workers. Thus, the appearance of this type of bifurcation is the result of assumed exogenous model symmetry. We provide a general analysis in a regional model of the class of bifurcations that have crossing equilibrium loci, including the tomahawk bifurcation, by examining arbitrary smooth parameter paths in a higher dimensional parameter space. We find that, in a parameter space satisfying a mild rank condition, generically in all parameter paths this class of bifurcations does not appear. In other words, conclusions drawn from the use of this bifurcation to generate a core-periphery pattern are not robust. Generically, this class of bifurcations is a myth, an urban legend.

Keywords: Bifurcation; Genericity Analysis; Migration Dynamics (search for similar items in EconPapers)
JEL-codes: F12 C61 R23 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-geo, nep-mig and nep-ure
Date: 2009-01-28
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Related works:
Journal Article: Bifurcations in regional migration dynamics (2009) Downloads
Working Paper: Bifurcations in regional migration dynamics (2004) Downloads
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