Talk:Shilnikov saddle-node bifurcation
I like the text and (in particular) the figures. However, it might be useful to explicitly include one bifurcation parameter and stress that the considered phenomenon has codim 1. In this line, it should be mentioned that the given normal form is the critical normal form.
The parameter was introduced and comments that the bifurcation is yet of codimension-1 are made.
Please, also collect all historical remarks and discussions of Lorenz-like cases to a separate section.
I also miss a reference to
Champneys, Alan R., Härterich, Jörg, Sandstede, Björn. A non-transverse homoclinic orbit to a saddle-node equilibrium. Ergodic Theory Dynam. Systems 16 (1996), no. 3, 431--450.
where it has been shown that a generalized Henon map appears as the principle part of the Poincare map near the critical homoclinic orbit.
This suggested reference is added. Thank you for pointing it out.
This well-written adequately short article is ready to be published in Scholarpedia. I have a couple of small remarks: 4 line from above: affter this=>due to Fig 1 capture: Stable manifolds=>stable sets (stable and unstable manifolds are one-dimensional whiile stable and unstable sets are two-dimensional). Formulation of theorem 2: Not W_u intersection W_u but W_u intersection W_s ; the same for dW. Formulation of Theorem 3: add somewhere, for example before of the words 'is born" or in an appropriate place : "in a neighborhood of the collection of the homoclinic trajectories Gamma_1,...Gamma_m"