Bifurcations in the regularized Ericksen bar model

Details Bifurcations in the regularized Ericksen bar model Bifurcations in the regularized Ericksen bar model

2007-11-08

arxiv.org/abs/0711.1257v2

Mathematics

Dynamical Systems

Scientific paper

We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation methods, the structure of bifurcations from double zero eigenvalues. Our results provide evidence in support of M\"uller's conjecture \cite{Muller} concerning the symmetry of local minimizers of the associated energy functional and describe in detail the structure of the primary branch connections that occur in this problem. We give a reformulation of M\"uller's conjecture and suggest two further conjectures based on the local analysis and numerical observations. We conclude by analysing a ``loop'' structure that characterizes $(k,3k)$ bifurcations.

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