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1999 | 81 | 2 | 285-292
Tytuł artykułu

On peaks in carrying simplices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A necessary and sufficient condition is given for the carrying simplex of a dissipative totally competitive system of three ordinary differential equations to have a peak singularity at an axial equilibrium. For systems of Lotka-Volterra type that result translates into a simple condition on the coefficients.
Słowa kluczowe
Rocznik
Tom
81
Numer
2
Strony
285-292
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-03-08
Twórcy
  • Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
  • [1] E. Akin, The General Topology of Dynamical Systems, Grad. Stud. Math. 1, Amer. Math. Soc., Providence, RI, 1993.
  • [2] M. Benaïm, On invariant hypersurfaces of strongly monotone maps, J. Differential Equations 137 (1997), 302-319.
  • [3] P. Brunovský, Controlling nonuniqueness of local invariant manifolds, J. Reine Angew. Math. 446 (1994), 115-135.
  • [4] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Regional Conf. Ser. in Math. 38, Amer. Math. Soc., Providence, RI, 1978.
  • [5] J. K. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys Mono- graphs 25, Amer. Math. Soc., Providence, RI, 1988.
  • [6] M. W. Hirsch, Systems of differential equations which are competitive or cooperative. III. Competing species, Nonlinearity 1 (1988), 51-71.
  • [7] M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Math. 583, Springer, Berlin, 1977.
  • [8] J. Mierczyński, The $C^1$ property of carrying simplices for a class of competitive systems of ODEs, J. Differential Equations 111 (1994), 385-409.
  • [9] J. Mierczyński, On smoothness of carrying simplices, Proc. Amer. Math. Soc. 127 (1999), 543-551.
  • [10] J. Mierczyński, Smoothness of carrying simplices for three-dimensional competitive systems: A counterexample, Dynam. Contin. Discrete Impuls. Systems 6 (1999), 149-154.
  • [11] --, Smoothness of unordered invariant curves for two-dimensional strongly competitive systems, Appl. Math. (Warsaw) 25 (1999), 449-455.
  • [12] I. Tereščák, Dynamics of $C^1$ smooth strongly monotone discrete-time dynamical systems, preprint.
  • [13] M. L. Zeeman, Hopf bifurcations in competitive three-dimensional Lotka-Volterra systems, Dynam. Stability Systems 8 (1993), 189-217.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv81i2p285bwm
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