A cooperative system which does not satisfy the limit set dichotomy
动力系统
2007-05-23 v1 最优化与控制
摘要
The fundamental property of strongly monotone systems, and strongly cooperative systems in particular, is the limit set dichotomy due to Hirsch: if x(0) < y(0), then either omega(x) < omega(y), or omega(x) = omega(y) and both sets consist of equilibria. We provide here a counterexample showing that this property need not hold for (non-strongly) cooperative systems.
引用
@article{arxiv.math/0505271,
title = {A cooperative system which does not satisfy the limit set dichotomy},
author = {Eduardo D. Sontag and Yuan Wang},
journal= {arXiv preprint arXiv:math/0505271},
year = {2007}
}