Catastrophes of codimension three

A complete classification of the catastrophes in two state variables of codimension three has not yet been developed. Consequently, only the standard form of a catastrophe corresponding to the sensitive state of the Takens-Bogdanov bifurcation will be given. The generalized Takens--Bogdanov bifurcation has the corresponding standard form  

A description of dynamics and bifurcation diagrams for this catastrophe have been given by Medved. 

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