Genericity analysis of split bifurcations

Fan-chin Kung
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Fan-chin Kung: Academia Sinica

GE, Growth, Math methods from University Library of Munich, Germany

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.

Keywords: Bifurcation; Genericity analysis; Regular parameterization; Migration dynamics (search for similar items in EconPapers)
JEL-codes: C60 F12 R23 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2004-10-13, Revised 2004-11-24
New Economics Papers: this item is included in nep-geo
Note: Type of Document - pdf; pages: 24
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpge:0410008

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