Edge formation in low-dimensional models of shear transition

Low dimensional models are used to illustrate the nature of an edge state. In these models the edge is the stable manifold of a lower-branch equilibrium point. It comes into existence in connection with the birth of a periodic orbit via a homoclinic bifurcation as a parameter (the Reynolds number) increases beyond a critical value. Even for values of the Reynolds number less than this critical value, the structure of the basin boundary is such that edge-like behavior occurs in parts of phase space. It is possible to manufacture dynamical systems for which the edge state disappears for sufficiently large parameter values.