Figure 27.

A, Coexistence of DB and RSE. The simulations are performed without noise. The equilibrium point of DB and a stable LC coexist for m = −8 and x₀ = −0.6. Trajectory segments are numbered in A and B. DB corresponds to the segment 4, and the NS to the segment 2. The equilibrium point of DB exists. The equilibrium point of NS does not. After a transient NS, the Epileptor stabilizes on DB. The arrows indicate the direction of trajectories. For easier visualization, we plot generalized coordinates (X, Y) corresponding to ($-10x_1+x_2,\hspace{0.17em}5y_1$) for DB (top) and to ($-0.6x_1+x_2,\hspace{0.17em}0.2y_1$) for LC (bottom). LC is characteristic of RSE. B, C, Time series of DB (B) and LC (C). Parameter settings correspond to region V in Figure 34 and to region 9 of 5 in Figure 35. A, Top, I.C = [−0.1 −6 3.8 0 0 0.01], T_s = [0 400], and r  =  0.01. A, Bottom, I.C = [9 −5 −1 0 0 0.01], T_s = [0 200], and r  =  0.009. The coexistence of LC and S can be found in area II (Fig. 12B).