Path formulation for a modal family

      Abstract
      Persistent bifurcation diagrams in unfoldings of the modal family $g(x,\lambda)=\varepsilon x^{4}+2ax^{2}\lambda+\delta\lambda^{2}$ 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.

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