Genericity analysis of split bifurcations
This paper analyzes the genericity of bifurcations of one-parameter families of smooth (C1) vector fields that are embedded in an underlying multi-dimensional parameter space. Bifurcations with crossing equilibrium loci are called 'split bifurcations.' They include, for example, the pitchfork bifurcation and the transcritical bifurcation. In a regular parameter space where the system's Jacobian matrix with respect to endogenous variables and parameters has full rank at every equilibrium for all parameter values, there is a generic (open and dense) set of one-parameter C1 families of vector fields without split bifurcations. It is not difficult to obtain a regular parameter space when there are enough parameters. A regional migration model (a la Fujita, Krugman and Venables 1999) featuring the pitchfork bifurcation is presented as an example.
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- Berliant, Marcus & Kung, Fan-chin, 2006.
"The indeterminacy of equilibrium city formation under monopolistic competition and increasing returns,"
Journal of Economic Theory,
Elsevier, vol. 131(1), pages 101-133, November.
- Marcus Berliant & Fan- chin Kung, 2004. "The Indeterminacy of Equilibrium City Formation under Monopolistic Competition and Increasing Returns," Urban/Regional 0407011, EconWPA, revised 29 Apr 2005.
- Mas-Colell,Andreu, 1990.
"The Theory of General Economic Equilibrium,"
Cambridge University Press, number 9780521388702, December.
- Fujita, Masahisa & Mori, Tomoya, 1997. "Structural stability and evolution of urban systems," Regional Science and Urban Economics, Elsevier, vol. 27(4-5), pages 399-442, August.
- Paul Krugman, 1990.
"Increasing Returns and Economic Geography,"
NBER Working Papers
3275, National Bureau of Economic Research, Inc.
- DEBREU, Gérard, .
"Economies with a finite set of equilibria,"
CORE Discussion Papers RP
67, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Marcus Berliant & Yves Zenou, 2004.
"Labor Differentiation and Agglomeration in General Equilibrium,"
- Marcus Berliant & Yves Zenou, 2014. "Labor Differentiation and Agglomeration in General Equilibrium," International Regional Science Review, SAGE Publishing, vol. 37(1), pages 36-65, January.
- Berliant, Marcus & Zenou, Yves, 2012. "Labor Differentiation and Agglomeration in General Equilibrium," CEPR Discussion Papers 8840, C.E.P.R. Discussion Papers.
- Berliant, Marcus & Zenou, Yves, 2012. "Labor differentiation and agglomeration in general equilibrium," MPRA Paper 36207, University Library of Munich, Germany.
- Masahisa Fujita & Paul Krugman & Anthony J. Venables, 2001. "The Spatial Economy: Cities, Regions, and International Trade," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262561476, March.
- Timothy J. Kehoe, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, Oxford University Press, vol. 100(1), pages 119-147.
- Antinolfi, Gaetano & Keister, Todd & Shell, Karl, 2001. "Growth Dynamics and Returns to Scale: Bifurcation Analysis," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 70-96, January.
- Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, March.
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