Berliant, Marcus and Kung, Fanchin (2009): Bifurcations in Regional Migration Dynamics.

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Abstract
The tomahawk bifurcation is used by Fujita et al. (1999) in a model with two regions to explain the formation of a coreperiphery 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 coreperiphery pattern are not robust. Generically, this class of bifurcations is a myth, an urban legend.
Item Type:  MPRA Paper 

Original Title:  Bifurcations in Regional Migration Dynamics 
Language:  English 
Keywords:  Bifurcation; Genericity Analysis; Migration Dynamics 
Subjects:  F  International Economics > F1  Trade > F12  Models of Trade with Imperfect Competition and Scale Economies ; Fragmentation C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis R  Urban, Rural, Regional, Real Estate, and Transportation Economics > R2  Household Analysis > R23  Regional Migration ; Regional Labor Markets ; Population ; Neighborhood Characteristics 
Item ID:  13053 
Depositing User:  Marcus Berliant 
Date Deposited:  29. Jan 2009 05:07 
Last Modified:  12. Feb 2013 11:47 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/13053 