On the ω-limit Set Dichotomy of Cooperating Kolmogorov Systems
نویسندگان
چکیده
The authors study the ω-limit set dichotomy of the Kolmogorov systems ẋi = xifi(x), xi 0, 1 i n with the cooperative and irreducible hypotheses and obtain the quasiconvergence almost everywhere when n = 3, which gives an affirmative answer to the open problem by Smith [9, p.72] in the case of n = 3.
منابع مشابه
1 2 M ay 2 00 5 A cooperative system which does not satisfy the limit set dichotomy Eduardo
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 ω(x) < ω(y), or ω(x) = ω(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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