Institute of Mathematics, Wroclaw University of Technology, Wybrzeze Wyspian- skiego 27, PL-50-370 Wroclaw, Poland
Abstract:
We consider dissipative strongly competitive systems of ordinary differential equations. It is known that for a wide class of such systems there exists an invariant attracting hypersurface , called the carrying simplex. In this note we give an amenable condition for to be a submanifold-with-corners. We also provide conditions, based on a recent work of M. Benaïm (On invariant hypersurfaces of strongly monotone maps, J. Differential Equations 136 (1997), 302-319), guaranteeing that is of class .