Figure 3

A typical phase portrait of the reduced system (8). Fixed points of the desingularized system (9) are denoted by crosses, \(x_{l}\) is a stable node, \(x_{m}\) and \(x_{h}\) are saddle points and \(x_{f}\) is a folded focus (unstable). Stable and unstable manifolds of the saddle points are shown in blue and red, respectively. Along the two lines of folds \(F_{l}\) and \(F_{h}\) the system is singular: trajectory at those points are defined only in forward or backward time; the first of these two cases corresponds to jump points. The stable manifold of \(x_{m}\) separates initial conditions in \(S_{l}\) (left of \(F_{l}\)) that reach a jump point from those that converge to \(x_{l}\)