On Smoothness of Carrying Simplices

@inproceedings{Mierczynski1998OnSO,
  title={On Smoothness of Carrying Simplices},
  author={Janusz Mierczynski},
  year={1998}
}
We consider dissipative strongly competitive systems ẋi = xifi(x) of ordinary differential equations. It is known that for a wide class of such systems there exists an invariant attracting hypersurface Σ, called the carrying simplex. In this note we give an amenable condition for Σ to be a C1 submanifold-with-corners. We also provide conditions, based on a recent work of M. Benäım (On invariant hypersurfaces of strongly monotone maps, J. Differential Equations 136 (1997), 302–319), guaranteeing… CONTINUE READING

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