On Dynamics of Generalized Competitive and Cooperative Systems

In this paper, we are concerned with n-dimensional generalized competitive or cooperative systems of ordinary dierential equations. A result is established to show that the ow generated by a generalized cooperative and irreducible system is strongly monotone. Also, it is shown that an analogue of the Poincare-Bendixon theorem holds for three dimensional generalized competitive and dissipative systems. Finally, we provide a generalized Smale's construction.