Three-dimensional cooperative irreducible systems with a first integral

• Autorzy: Janusz Mierczyński
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 76
• Numer: 2
• Strony: 181-190

Daty

wydano

1998

otrzymano

1997-07-01

Twórcy

autor

Janusz Mierczyński

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

• [1] B. Grammaticos, J. Moulin-Ollagnier, A. Ramani, J.-M. Strelcyn and S. Wojciechowski, Integrals of quadratic ordinary differential equations in $ℝ^3$: The Lotka-Volterra system, Phys. A 163 (1990), 683-722.
• [2] M. W. Hirsch, Systems of differential equations which are competitive or cooperative. I. Limit sets, SIAM J. Math. Anal. 13 (1982), 167-179.
• [3] M. W. Hirsch, Systems of differential equations that are competitive or cooperative. II. Convergence almost everywhere, ibid. 16 (1985), 423-439.
• [4] M. W. Hirsch, Systems of differential equations which are competitive or cooperative. III. Competing species, Nonlinearity 1 (1988), 51-71.
• [5] M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Math. 583, Springer, Berlin, 1977.
• [6] J. Mierczyński, A class of strongly cooperative systems without compactness, Colloq. Math. 62 (1991), 43-47.
• [7] J. Palis and F. Takens, Topological equivalence of normally hyperbolic dynamical systems, Topology 16 (1977), 335-345.
• [8] H. L. Smith, Periodic orbits of competitive and cooperative systems, J. Differential Equations 65 (1986), 361-373.
• [9] H. L. Smith, Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys Monographs 41, Amer. Math. Soc., Providence, R.I., 1995.
• [10] I. Tereščák, Dynamics of $C^1$ smooth strongly monotone discrete-time dynamical systems, preprint.