How are normal forms, versal unfoldings and bifurcation types related?

01 January 2014 1 4K Report

Having a family of vector fields (non-linear, 2d), depending on several control parameters with degenerate fixed points for some values of these, how can we determine the bifurcation type from the normal form?

Jason Bramburger

Bifurcations have specific normal forms. In that sense, you do not traditionally find bifurcations using the normal form, you find the normal form of the bifurcation (close to the singularity.) From here you can find the specifics of the bifurcation, but everything rests on knowing the eigenvalues of the system linearized about a certain equilibrium.

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