Fig. 8

Quasi-bistability phenomenon. The CBA is used for the investigation of the quasi-bistability phenomenon, in which the system, despite being monostable, shows a very prolonged sustained response. The first column shows the time course of normalized ppERK for a representative parameter sample from class 2 with switching time at t _switch≈440 min. Columns 2,3 and 4 show the circuit-characteristic c(κ,u(t)), along with the actual normalized state ppERK(t) for 12 different time points. After a fast transient dynamic (a1) the circuit-characteristic has three zeros (A2-B1), which disappear at a later time point, here t=102 min (b2), via a saddle-node bifurcation. After 60 min the input is almost zero and the vector field and therefore the circuit-characteristic changes only slowly. The system state has almost approached the higher fixed point. b1-c3 are eyeglass views on the dynamics near this second fixed point. These plots show that, even if the fixed point has disappeared, the system trajectory moves very slowly through the state space for a rather long time, since \(\dot {x}\) is still small. Only after about 440 min the system has overcome this slow region of the state space, and from here on rapidly moves towards its globally asymptotically stable steady state \(\bar {x}=0\)