On the ω-limit Set Dichotomy of Cooperating Kolmogorov Systems

On the ω-limit Set Dichotomy of Cooperating Kolmogorov Systems The authors study the ω-limit set dichotomy of the Kolmogorov systems $$\dot x$$ i=xi f i(x)x i≥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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

On the ω-limit Set Dichotomy of Cooperating Kolmogorov Systems

, Volume 7 (3) – Oct 4, 2004
10 pages

/lp/springer_journal/on-the-limit-set-dichotomy-of-cooperating-kolmogorov-systems-TYki2g0W0Y
Publisher
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1026287609893
Publisher site
See Article on Publisher Site

Abstract

The authors study the ω-limit set dichotomy of the Kolmogorov systems $$\dot x$$ i=xi f i(x)x i≥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.

Journal

PositivitySpringer Journals

Published: Oct 4, 2004

References

• Stability and convergence in strongly monotone dynamical systems
Hirsch, M.W.

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