Figure 30.

A, Coexistence of nonoscillatory state and RSE. Here after a transient NS, the Epileptor enters into the nonoscillatory state. The simulations are performed without noise. The equilibrium point of the nonoscillatory state and a stable LC coexist for m = −1 and x₀ = −0.8 ($I_{ex{t}_2}=0$). Trajectory segments are numbered in A and B. The transient NS is indicated by (1) and the nonoscillatory state (final state) by (3). The equilibrium point of nonoscillatory state exists, which is a stable focus. After a transient NS, the Epileptor spirals into the equilibrium point (stable focus) and remains in the nonoscillatory state. The arrows indicate the direction of trajectories. For easier visualization, we plot generalized coordinates (X, Y) corresponding to ($-35x_1+x_2,\hspace{0.17em}15y_1$) for the nonoscillatory state (top) and to ($-0.5x_1+x_2,\hspace{0.17em}0.1y_1$) for LC (bottom). LC is characteristic of RSE. B, C, Time series of the nonoscillatory state (B) and LC (C). Parameter settings correspond to region V in Figure 34 and to region 6 in Figure 32. A, Top, I.C = [−1 −5.5 3.5 0 0 0.01], T_s = [0 200], and r  =  0.01. A, Bottom, I.C = [10 −5 −1 0 0 0.01], T_s = [0 250], and r  =  0.004. The coexistence of LC and S can be found in area II (Fig. 12B).