= 0\}$ with stopping condition $\dot{z} < 0$ and (b) the normalized time series of their normalized $y$-coordinates of each trajectory. Initial conditions: blue, $(x,y,z) = (0.000553, 0.000201, 0)$; red, $(x,y,z) = (0.000553, 0.003065, 0)$. Parameter set: $\nu \approx 0.00870134$, $a = 0.01$, $b = -1$, $c = 1$.](5bpng.png "fig:"){width="45.00000%"}

Trajectories beginning in $\Sigma_0$ either follow $W^s$ closely and spiral out along $W^u$ or remain a bounded distance away from both the equilibrium point and $W^s$, instead making small-amplitude oscillations consistent with a folded node. Differences between these two types of small-amplitude oscillations have been observed in earlier work. The transition from the first kind of small-amplitude oscillation to the second is a function of the distance from the initial condition to the intersection of $W^s$ with the cross-section. Two initial conditions are chosen on a vertical line embedded in the section $\{z=0\}$, having the property that the resulting trajectory jumps right from $S^r_{{ \varepsilon}}$ at an intermediate height before returning to the section with orientation $\dot{z} < 0$. These initial conditions are found by selecting points in Figure \[fig:z0\](b) in the blue regions lying on a ray that extends outward from the center of the repelling spiral. The corresponding 