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.
Publié le : 2006-03-14
Classification:
Competitive/cooperative system,
Smale's construction,
dynamics,
arbitrary order cone,
34C25,
34K25,
34C12
@article{1145390207,
author = {Huang, Lihong and Yi, Taishan and Zou, Xingfu},
title = {On Dynamics of Generalized Competitive and Cooperative Systems},
journal = {Tohoku Math. J. (2)},
volume = {58},
number = {1},
year = {2006},
pages = { 89-100},
language = {en},
url = {http://dml.mathdoc.fr/item/1145390207}
}
Huang, Lihong; Yi, Taishan; Zou, Xingfu. On Dynamics of Generalized Competitive and Cooperative Systems. Tohoku Math. J. (2), Tome 58 (2006) no. 1, pp. 89-100. http://gdmltest.u-ga.fr/item/1145390207/