A cooperative system which does not satisfy the limit set dichotomy

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75183The 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.Dynamical SystemsOptimization and Control34C12A cooperative system which does not satisfy the limit set dichotomytext