PORTUGALIAEMATHEMATICA
Vol. 58, No. 4, pp. 407-424 (2001)
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PORTUGALIAE MATHEMATICA Vol. 58, No. 4, pp. 407-424 (2001) |
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Path Formulation for A Modal FamilyManuela A.D. Aguiar, Sofia B.S.D. Castro and Isabel S. LabouriauFaculdade de Economia, Universidade do Porto,Rua Dr. Roberto Frias, 4200 Porto -- PORTUGAL E-mail: maguiar@fep.up.pt , sdcastro@fep.up.pt Centro de Matemática Aplicada, Universidade do Porto, Rua das Taipas, 135, 4050-600 Porto -- PORTUGAL Departamento de Matemática Aplicada, Faculdade de Ciências, Universidade do Porto, Rua das Taipas, 135, 4050-600 Porto -- PORTUGAL E-mail: islabour@fc.up.pt Abstract: Persistent bifurcation diagrams in unfoldings of the modal family $g(x,\lambda)=\varepsilon\,x^{4}+2\,a\,x^{2}\,\lambda+\delta\,\lambda^{2}$ are described using path formulation: each bifurcation problem in the unfoldings of $g$ is reinterpreted as a $\lambda$-parametrized path in the universal unfolding of $x^{4}$. The space of unfolding parameters for the modal family is divided into regions where bifurcation problems are contact-equivalent and the bifurcation diagrams for these persistent problems are shown. Keywords: Bifurcation; Path Formulation; Singularities. Classification (MSC2000): 34D10, 58F14. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2001 Sociedade Portuguesa de Matemática
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