论文信息 - On the ω-limit Set Dichotomy of Cooperating Kolmogorov Systems

On the ω-limit Set Dichotomy of Cooperating Kolmogorov Systems

AbstractThe authors study the ω-limit set dichotomy of the Kolmogorov systems $$\dot x$$ i=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.

Jifa Jiang | Yi Wang

[1] F. V. Vleck,et al. Stability and Asymptotic Behavior of Differential Equations , 1965 .

[2] P. Hartman. Ordinary Differential Equations , 1965 .

[3] Jiang Jifa,et al. The asymptotic behavior of models of cooperation with a concavity property , 2000 .

[4] M. Hirsch,et al. Cohomology of chain recurrent sets , 1988, Ergodic Theory and Dynamical Systems.

[5] M. Hirsch. Systems of di erential equations which are competitive or cooperative I: limit sets , 1982 .

[6] S. Murakami. Asymptotic behavior of solutions of ordinary differential equations , 1982 .

[7] M V Makarets,et al. SYSTEMS OF DIFFERENTIAL EQUATIONS , 1995 .

[8] M. Hirsch. Stability and convergence in strongly monotone dynamical systems. , 1988 .

[9] Hal L. Smith,et al. Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[10] M. Hirsch. Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere , 1985 .