Dynamical Systems in Neuroscience:

One-Dimensional Systems 77F(V)I=18I=17I=16I=15I=14I=13I=12I=11no equilibriabifurcationtwo equilibriatangentpointVstable equilibriaunstable equilibriaFigure 3.26: Saddle-node bifurcation: As the graph of the function F (V ) is lifted up,the stable and unstable equilibria approach each other, coalesce at the tangent point,and then disappear.saddle-nodenot saddle-nodeFVnon-hyperbolichyperbolichyperbolicnon-degenerate degenerate degeneratetransversalnot transversalnot transversalFigure 3.27: Geometrical illustration of the three conditions defining saddle-node bifurcations.Arrows denote the direction of displacement of the function F (V, I) as thebifurcation parameter I changes.