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Genericity analysis of split bifurcations

Fan-chin Kung
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Fan-chin Kung: Academia Sinica

GE, Growth, Math methods from EconWPA

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 R23 F12 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-geo
Date: 2004-10-13, Revised 2004-11-24
Note: Type of Document - pdf; pages: 24
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