A cooperative system which does not satisfy the limit set dichotomy

Eduardo D. Sontag; Yuan Wang

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A cooperative system which does not satisfy the limit set dichotomy

Eduardo D. Sontag·Yuan Wang

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Abstract

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.

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Eduardo D. Sontag, Yuan Wang. 2005-05-12. A cooperative system which does not satisfy the limit set dichotomy. https://arxiv.org/abs/math/0505271

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