Figure 46.

The ($z,x_1$) subsystem 1 bifurcation diagram with respect to z as m and x₀ vary. A, m  =  0.5 and x₀ = −1.6, transitions between upper and lower branches occur through a fold/Hopf bifurcation. B, m  =  2 and x₀ = −1.9, transitions between upper and lower branches occur through a fold/homoclinic bifurcation. C, m  =  2 and x₀ = −1.7, the fast-slow subsystem stabilizes before a homoclinic bifurcation occurs, giving rise to the stable limit cycle SLC₁. D, m  =  0 and x₀ = −2.6, the fast-slow subsystem stabilizes its stable node, which is the equilibrium point of the NS. The z-nullcline and $<x_1>$ curve do not intersect, hence NS exists and LC does not. r  =  0.0006, I.C = [−0.5 −5 2.831], and T_s = [0:0.01: 1120] for A; r  =  0.002, I.C = [0 −5 2], and T_s = [0:0.01: 1300] for B; r  =  0.003, I.C = [−1.5 −5 4], and T_s = [0:0.01: 600] for C; and r  =  0.002, I.C = [0 −5 2], and T_s = [0:0.01: 1000] for D.