Three-dimensional cooperative irreducible systems with a first integral

Janusz Mierczyński

Colloquium Mathematicae (1998)

  • Volume: 76, Issue: 2, page 181-190
  • ISSN: 0010-1354

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Mierczyński, Janusz. "Three-dimensional cooperative irreducible systems with a first integral." Colloquium Mathematicae 76.2 (1998): 181-190. <http://eudml.org/doc/210558>.

@article{Mierczyński1998,
author = {Mierczyński, Janusz},
journal = {Colloquium Mathematicae},
keywords = {three-dimensional cooperative irreducible systems; ordinary differential equations; first integral},
language = {eng},
number = {2},
pages = {181-190},
title = {Three-dimensional cooperative irreducible systems with a first integral},
url = {http://eudml.org/doc/210558},
volume = {76},
year = {1998},
}

TY - JOUR
AU - Mierczyński, Janusz
TI - Three-dimensional cooperative irreducible systems with a first integral
JO - Colloquium Mathematicae
PY - 1998
VL - 76
IS - 2
SP - 181
EP - 190
LA - eng
KW - three-dimensional cooperative irreducible systems; ordinary differential equations; first integral
UR - http://eudml.org/doc/210558
ER -

References

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  1. [1] B. Grammaticos, J. Moulin-Ollagnier, A. Ramani, J.-M. Strelcyn and S. Wojciechowski, Integrals of quadratic ordinary differential equations in 3 : The Lotka-Volterra system, Phys. A 163 (1990), 683-722. Zbl0714.34005
  2. [2] M. W. Hirsch, Systems of differential equations which are competitive or cooperative. I. Limit sets, SIAM J. Math. Anal. 13 (1982), 167-179. Zbl0494.34017
  3. [3] M. W. Hirsch, Systems of differential equations that are competitive or cooperative. II. Convergence almost everywhere, ibid. 16 (1985), 423-439. 
  4. [4] M. W. Hirsch, Systems of differential equations which are competitive or cooperative. III. Competing species, Nonlinearity 1 (1988), 51-71. Zbl0658.34024
  5. [5] M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Math. 583, Springer, Berlin, 1977. 
  6. [6] J. Mierczyński, A class of strongly cooperative systems without compactness, Colloq. Math. 62 (1991), 43-47. Zbl0737.34032
  7. [7] J. Palis and F. Takens, Topological equivalence of normally hyperbolic dynamical systems, Topology 16 (1977), 335-345. 
  8. [8] H. L. Smith, Periodic orbits of competitive and cooperative systems, J. Differential Equations 65 (1986), 361-373. Zbl0615.34027
  9. [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. Zbl0821.34003
  10. [10] I. Tereščák, Dynamics of C 1 smooth strongly monotone discrete-time dynamical systems, preprint. 

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