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Genericity analysis of split bifurcations

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Author Info
Fan-chin Kung (Academia Sinica)
Abstract

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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Paper provided by EconWPA in its series GE, Growth, Math methods with number 0410008.

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Length: 24 pages
Date of creation: 13 Oct 2004
Date of revision: 13 Oct 2004
Handle: RePEc:wpa:wuwpge:0410008

Note: Type of Document - pdf; pages: 24
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Related research
Keywords: Bifurcation; Genericity analysis; Regular parameterization; Migration dynamics;

Find related papers by JEL classification:
C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General
R23 - Urban, Rural, and Regional Economics - - Household Analysis - - - Regional Migration; Regional Labor Markets; Population
F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Marcus Berliant & Yves Zenou, 2004. "Labor Differentiation and Agglomeration in General Equilibrium," Urban/Regional 0408003, EconWPA. [Downloadable!]
  2. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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.
  5. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June. [Downloadable!] (restricted)
    Other versions:
  6. Kehoe, Timothy J, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, MIT Press, vol. 100(1), pages 119-47, February. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215.
  9. 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. [Downloadable!]
    Other versions:
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Marcus Berliant, 2005. "Well Isn't That Spatial?! Handbook of Regional and Urban Economics: A View From Economic Theory," Urban/Regional 0503001, EconWPA, revised 08 Apr 2005. [Downloadable!]
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