ON DYNAMICS OF GENERALIZED COMPETITIVE AND COOPERATIVE SYSTEMS
2006 Volume 58 Issue 1 Pages 89-100
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2006 Volume 58 Issue 1 Pages 89-100
In this paper, we are concerned with $n$-dimensional generalized competitive or cooperative systems of ordinary differential equations. A result is established to show that the flow generated by a generalized cooperative and irreducible system is strongly monotone. Also, it is shown that an analogue of the Poincarè-Bendixon theorem holds for three dimensional generalized competitive and dissipative systems. Finally, we provide a generalized Smale's construction.
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