  Transversality of stable and unstable manifolds of hyperbolic periodic
trajectories is proved for monotone cyclic systems with negative feedback. Such
systems in general are not in the category of monotone dynamical systems in the
sense of Hirsch. Our main tool utilized in the proofs is the so-called cone of
high rank. We further show that stable and unstable manifolds between a
hyperbolic equilibrium and a hyperbolic periodic trajectory, or between two
hyperbolic equilibria with different dimensional unstable manifolds also
intersect transversely.
