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Genericity analysis of split bifurcations

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  • 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.

Suggested Citation

  • Fan-chin Kung, 2004. "Genericity analysis of split bifurcations," GE, Growth, Math methods 0410008, University Library of Munich, Germany, revised 24 Nov 2004.
    • Handle: RePEc:wpa:wuwpge:0410008
    Note: Type of Document - pdf; pages: 24
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ge/papers/0410/0410008.pdf
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    References listed on IDEAS

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    7. 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.
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    Cited by:

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

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    More about this item

    Keywords

    Bifurcation; Genericity analysis; Regular parameterization; Migration dynamics;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • R23 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Regional Migration; Regional Labor Markets; Population
    • F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies; Fragmentation

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