An n-dimensional competitive Lotka-Volterra system is generically determined by the edges of its carrying simplex

Nonlinearity

Volumn 15, Issue 6, 2002, Pages 2019-2032

  Zeeman, E C ^a   Zeeman, M L ^b  

^a HERTFORD COLLEGE   (United Kingdom)

^b UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042035645     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/15/6/312     Document Type: Article

References (9)

1. Hirsch M W 1988 Systems of differential equations that are competitive or cooperative: III. Competing species Nonlinearity 1 51-71
2. Hofbauer J and Sigmund K 1988 Evolutionary Games and Population Dynamics (Cambridge: Cambridge University Press)
3. Plank M 1996 Bi-Hamiltonian systems and Lotka-Volterra equations: a three-dimensional classification Nonlinearity 9 887-96
4. Plank M 1999 On the dynamics of Lotka-Volterra equations having an invariant hyperplane SIAM J. Appl. Math. 59 1540-51
5. van den Driessche P and Zeeman M L 1998 Three-dimensional competitive Lotka-Volterra systems with no periodic orbits SIAM J. Appl. Math. 58 227-34
6. Zeeman E C and Zeeman M L 1994 On the convexity of carrying simplices in competitive Lotka-Volterra systems Differential Equations, Dynamical Systems, and Control Science (Lecture Notes in Pure Appl. Math. vol 152) (New York: Dekker) pp 353-64
7. Zeeman E C and Zeeman M L 2002 From local to global behaviour in competitive Lotka-Volterra systems Trans. AMS to appear
8. Zeeman E C 2002 Classification of quadratic carrying simplices in two-dimensional competitive Lotka-Volterra systems Nonlinearity 15 1993-2018
9. Zeeman M L 1993 Hopf bifurcations in competitive three dimensional Lotka-Volterra systems Dynam. Stab. Sys. 8 189-217