Smoothness of carrying simplices for three-dimensional competitive systems: A counterexample

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm

Volumn 6, Issue 1, 1999, Pages 147-154

  Mierczyński, Janusz ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

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EID: 0013262816     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. M. Benaïm, On invariant hypersurfaces of strongly monotone maps, J. Differential Equations, 136, (1997), 302-319.
2. P. Brunovský, Controlling nonuniqueness of local invariant manifolds, J. Reine Angew. Math., 446, (1994), 115-135.
3. J. K. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr., 25, Amer. Math. Soc., Providence, RI, 1988.
4. P. Hartman, Ordinary Differential Equations, Wiley, New York-London-Sydney, 1964.
5. M. W. Hirsch, Systems of differential equations which are competitive or cooperative. I. Limit sets, SIAM J. Math. Anal., 13, (1982), 167-179.
6. M. W. Hirsch, Systems of differential equations that are competitive or cooperative. II. Convergence almost everywhere, SIAM J. Math. Anal., 16, (1985), 423-439.
7. M. W. Hirsch, Systems of differential equations which are competitive or cooperative. III. Competing species, Nonlinearity 1, (1988), 51-71.
8. M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Math. 583, Springer, Berlin-New York, 1977.
9. J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems, London Mathematical Society Student Texts, 7, Cambridge University Press, Cambridge, 1988.
10. 1 property of carrying simplices for a class of competitive systems of ODEs, J. Differential Equations, 111, (1994), 385-109.
11. J. Mierczyński, On smoothness of carrying simplices, Prov. Amer. Math. Soc., to appear.
12. E. Seneta, Non-negative Matrices and Markov Chains (Second Edition), Springer Ser. Statist., Springer, New York-Heidelberg-Berlin, 1981.
13. 1 smooth strongly monotone discrete-time dynamical systems, preprint.
14. M. L. Zeeman, Hopf bifurcations in competitive three-dimensional Lotka-Volterra systems, Dynam. Stability Systems, 8, (1993), 189-217.