Fig. 9

Combination of two delay mechanisms in quasi-bistable systems. a Scheme of a bifurcation diagram for a quasi-bistable system. The system is monostable for u=0 and has a saddle-node bifurcation u ^SNB close to u=0, where it becomes bistable. A sufficiently strong transient signal u(t) pushes the system state into the basin of attraction of the higher stable steady state (1). As long as the change in u(t) is not slow compared to the dynamics of the system, the system cannot be considered in quasi-steady state, and we observe a transient dynamics (2). When u(t) is almost back to 0, two delay effects lead to quasi-bistable behavior (3). First, the system remains in the upper stable steady state as long as u(t) is still above the saddle-node bifurcation. Second, for u(t)<u ^SNB the acceleration remains very small in this region of the state space. b Absolute value of the vector field along the model trajectory for the same model parameters that have been used in Fig. 8. c Two respresentative bifurcation diagrams for a quasi-bistable system belonging to class 2 of the classification scheme, and a bistable system belonging to class 1