Formulation of a computational asymptotic bifurcation theory applicable to hill-top branching and multiple bifurcation analyses

Imperfection sensitivity analysis of hill-top branching with many symmetric bifurcation points

Imperfection sensitivity properties are derived for finite dimensional elastic conservative systems exhibiting hill-top branching at which arbitrary many bifurcation points coincide with a limit point. The critical load at a hill-top branching point is demonstrated to be insensitive to initial imperfections when all the bifurcation points are individually symmetric. Therefore, it is not dangero...

The Path Formulation of Bifurcation Theory

We show how the path formulation of bifurcation theory can be made to work, and that it is (essentially) equivalent to the usual parametrized contact equivalence of Golubitsky and Schaeeer.

Introduction to bifurcation theory

The theory of bifuxcation from equilibria based on center-manifold reduction and Poincare-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived. The emphasis is on the simplest generic bifurcations in one-parameter systems. Two applications are developed in detail:...

An introduction to bifurcation theory

The aim of this chapter is to introduce tools from bifurcation theory which will be necessary in the following sections for the study of neural field equations (NFE) set in the primary visual cortex. In a first step, we deal with elementary bifurcations in low dimensions such as saddle-node, transcritical, pitchfork and Hopf bifurcations. NFEs are dynamical systems defined on Banach spaces and ...

Computational Bifurcation WOB — Tutorial 4 R . Seydel World of Bifurcation