I am seeking a general algorithm to prove the existence of saddle-node, transcritical and pitchfork bifurcation for a 3D model.
Please provide some notes on this topic. Thanks in advance!
2026-03-26 22:57:55.1774565875
Analytical proofs of saddle node, transcritical and pitchfork bifurcation in 3D
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There is no general "algorithm" for bifurcation classification. However, several local bifurcations --i.e. bifurcations which can be detected simply through the stability analysis of equilibrium points-- have a normal form, which makes it possible for them to be identified (see e.g. [1]). A typical example on which this method applies is the Lorenz system [2].