On the Existence and Uniqueness of Connecting Orbits for Cooperative Systems

This paper considers the problem of the existence and uniqueness of the connecting orbit for a cooperative vector Beld F in the retangular box B. Suppose that the origin O and the point P with positive components are vertices of B, only containing the equilibria O and P. and that the Jacobian matrices of Fat 0 and P are irreducible. Then there is a unique orbit of F contained in B which joins O and P.