A Lyapunov function for tridiagonal competitive-cooperative systems

Authors
Fiedler, B Gedeon, T
Citation
B. Fiedler et T. Gedeon, A Lyapunov function for tridiagonal competitive-cooperative systems, SIAM J MATH, 30(3), 1999, pp. 469-478
Citations number
14
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN journal
00361410 → ACNP
Volume
30
Issue
3
Year of publication
1999
Pages
469 - 478
Database
ISI
SICI code
0036-1410(19990409)30:3<469:ALFFTC>2.0.ZU;2-N
Abstract
We construct a Lyapunov function for tridiagonal competitive-cooperative sy stems. The same function is a Lyapunov function for Kolmogorov tridiagonal systems, which are defined on a closed positive orthant in R-n. We show tha t all bounded orbits converge to the set of equilibria. Moreover, we show t hat there can be no heteroclinic cycles on the boundary of the first orthan t, extending the results of H. I. Freedman and H. L. Smith [Differential Eq uations Dynam. Systems, 3 (1995), pp. 367-382].