In contrast to the previous examples, it is difficult to define a threshold without an unstable saddle point which defines a separatrix. For the deterministic limit, a threshold can be defined in certain limits \cite{khovanov13a}, but there is no general structural definition and often ad-hoc excitation thresholds are defined. However, a stochastic analysis of MPPs shows that the excitable system with one fixed point shares many features in common with the system with three fixed points.