  We study a simple dynamical model exhibiting sequential dynamics. We show
that in this model there exist sets of parameter values for which a cyclic
chain of saddle equilibria, $O_k$, $k=1, \ldots, p$, have two dimensional
unstable manifolds that contain orbits connecting each $O_k$ to the next two
equilibrium points $O_{k+1}$ and $O_{k+2}$ in the chain ($O_{p+1} = O_1$). We
show that the union of these equilibria and their unstable manifolds form a
$2$-dimensional surface with boundary that is homeomorphic to a cylinder if $p$
is even and a M\"{o}bius strip if $p$ is odd. If, further, each equilibrium in
the chain satisfies a condition called ``dissipativity," then this surface is
asymptotically stable.
