  A standard result by Smale states that n dimensional strongly cooperative
dynamical systems can have arbitrary dynamics when restricted to unordered
invariant hyperspaces. In this paper this result is extended to the case when
all solutions of the strongly cooperative system are bounded and converge
towards one of only two equilibria outside of the hyperplane.
  An application is given in the context of strongly cooperative systems of
reaction diffusion equations. It is shown that such a system can have a
continuum of spatially inhomogeneous steady states, even when all solutions of
the underlying reaction system converge to one of only three equilibria.
