Systems of differential equations that are competitive or cooperative. VI: A localCrClosing Lemma for 3-dimensional systems

For certain C r 3-dimensional cooperative or competitive vector fields F , where r is any positive integer, it is shown that for any nonwandering point p , every neighborhood of F in the C r topology contains a vector field for which p is periodic, and which agrees with F outside a given neighborhood of p . The proof is based on the existence of invariant planar surfaces through p .