What is a Bifurcation Manifold?

 

Away from singularities, the solution set of
 

f(x;p) = 0, f:Rn x Rm --> Rn

is an m-dimensional manifold embedded in Rn+m.

The union of these manifolds, along with their singularities, intersections, etc is what we call the Bifurcation Manifold, and we call any representation or visualization of the Bifurcation Manifold, a Bifurcation Diagram.


 
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