CONVERGENCE TO TRAP ALMOST EVERYWHERE FOR FLOWS GENERATED BY COOPERATIVE AND IRREDUCIBLE VECTOR FIELDS
Citation：
Jiang Jifa.CONVERGENCE TO TRAP ALMOST EVERYWHERE FOR FLOWS GENERATED BY COOPERATIVE AND IRREDUCIBLE VECTOR FIELDS[J].Chinese Annals of Mathematics B,1993,14(2):165~174
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Authors：
Jiang Jifa;
Abstract：
This paper is concerned with the asymptotic behavior of cooperative systems in $W\subset R^n$. For a $C^2$ cooperative system whose Jacobian matrices are irreducible, it is proved that the forward orbit converges to an equilibrium for almost every point having compact forward orbit closure and the set of all points which have compact forward orbit closures and do not converge to a semi-asymptotically stable equilibrium is meager in W if the equilibrium set cannot contain a simply ordered curve. The invariant function and the geometry of the stable manifold of an unstable equilibrium are considered.
