“…Nowadays, with the development of new experimental techniques, it has been possible to observe local unstable equilibria or transient excited states in numerous physical/chemical/biological systems. Consequently, their theoretical and numerical studies have attracted increasing attentions [2,4,15,21,27,30]. However, these local unstable equilibria or transient excited states are related to critical points that are not local extrema, and then called saddle points.…”