  In the paper [Large-amplitude periodic solutions for differential equations
with delayed monotone positive feedback, JDDE 23 (2011), no. 4, 727--790], we
have constructed large-amplitude periodic orbits for an equation with delayed
monotone positive feedback. We have shown that the unstable sets of the
large-amplitude periodic orbits constitute the global attractor besides
spindle-like structures. In this paper we focus on a large-amplitude periodic
orbit $\mathcal{O}_{p}$ with two Floquet multipliers outside the unit circle,
and we intend to characterize the geometric structure of its unstable set
$\mathcal{W}^{u}\left(\mathcal{O}_{p}\right)$. We prove that
$\mathcal{W}^{u}\left(\mathcal{O}_{p}\right)$ is a three-dimensional
$C^{1}$-submanifold of the phase space and admits a smooth global graph
representation. Within $\mathcal{W}^{u}\left(\mathcal{O}_{p}\right)$, there
exist heteroclinic connections from $\mathcal{O}_{p}$ to three different
periodic orbits. These connecting sets are two-dimensional $C^{1}$-submanifolds
of $\mathcal{W}^{u}\left(\mathcal{O}_{p}\right)$ and homeomorphic to the
two-dimensional open annulus. They form $C^{1}$-smooth separatrices in the
sense that they divide the points of
$\mathcal{W}^{u}\left(\mathcal{O}_{p}\right)$ into three subsets according to
their $\omega$-limit sets.
