Figure 35.

The Epileptor parameter space of equilibrium points and periodic orbits with respect to the parameters m and x₀ ($I_{ext2}=0$). There are 20 regions separated by a SNPO bifurcation (bold line). LC exists above and it does not exist below. The z-nullcline intersects the (z, x₁) curve at different equilibrium points. The equilibrium point is an unstable focus for areas 1 through 3. The equilibrium points are a stable node, an unstable focus, and a saddle in areas 4 and 5. The equilibrium points are a stable focus, an unstable focus, and a saddle in area 6. The equilibrium points are one saddle and two unstable foci in area 7. The equilibrium point is a stable node in areas 8, 9, 11, 19, and 20. The equilibrium point is a stable focus in area 10. The equilibrium point is a saddle for areas 12 through 18. In areas 1, 7, and 17, only LC exists. Areas 2 and 18 present bistability of LC and SLC. In area 3, only SLC exists. In areas 4 and 8, only DB exists. In areas 5 and 9, LC and DB coexist. In areas 6, 10, and 11, LC and nonoscillatory state coexist. Only a periodic switch between DB and NS exists in area 12, and coexists with LC in area 13. A periodic switch between a nonoscillatory state and NS coexists with LC in area 14. LC and SLE coexist in areas 15 and 16. SLE occurs through a fold/Hopf bifurcation in area 15 and through a fold/homoclinic bifurcation in area 16. NS exists in area 19 and coexists with LC in area 20.