On a Lotka-Volterra model which can be projected to a sphere

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 3, 1997, Pages 1405-1410

  Uno, Tamiyuki ^a   Odani, Kenzi ^b  

^a NAGOYA UNIVERSITY   (Japan)

^b AICHI UNIVERSITY OF EDUCATION   (Japan)

Author keywords

Application of vector analysis; Existence of nonconstant analytic first integral; Generalized May Leonard model; Lot ka Volterra model of 3 species; Nonexistence of closed orbits

Indexed keywords

EID: 0000926545     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00201-0     Document Type: Article

References (9)

1. N. N. Bautin, On periodic solutions of a system of differential equations, Prikl. Mat. Mekh. 18 (1954), 128. [Russian]
2. A. Chenciner, Comportent asymptotique de systèmes differentiels du type "compétition d'espèces", C. R. Acad. Sc. Paris 284A (1977), 313-315.
3. C.-W. Chi, S.-B. Hsu and L.-I. Wu, On the asymmetric May-Leonard model of three competing species, SIAM J. Appl. Math., to appear.
4. J. Coste, J. Peyraud and P. Coullet, Asymptotic behaviors in the dynamics of competing species, SIAM J. Appl. Math. 36 (1979), 517-543.
5. J. E. Franke and J. F. Selgrade, Abstract omega-limit sets, chain recurrent sets, and basic sets for flows, Proc. Amer. Math. Soc. 60 (1976), 309-316.
6. J. Hofbauer and K. Sigmund, "The Theory of Evolution and Dynamical Systems", Cambridge Univ. Press, Cambridge / New York, 1988.
7. R. May and W. J. Leonard, Nonlinear aspects of competition between species, SIAM J. Appl. Math. 29 (1975), 243-275.
8. P. Schuster, K. Sigmund and R. Wolf, On ω-limit for competition between three species, SIAM J. Appl. Math. 37 (1979), 49-54.
9. M. L. Zeeman, Extinction in competitive Lotka-Volterra systems, Proc. Amer. Math. Soc. 123 (1995), 87-96.