Bounding the number of cycles of ODES in R-n

Authors
Farkas, M Van Den Driessche, P Zeeman, ML
Citation
M. Farkas et al., Bounding the number of cycles of ODES in R-n, P AM MATH S, 129(2), 2000, pp. 443-449
Citations number
15
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
129
Issue
2
Year of publication
2000
Pages
443 - 449
Database
ISI
SICI code
0002-9939(2000)129:2<443:BTNOCO>2.0.ZU;2-C
Abstract
Criteria are given under which the boundary of an oriented surface does not consist entirely of trajectories of the C-1 differential equation (x) over dot = f(x) in R-n. The special case of an annulus is further considered, a nd the criteria are used to deduce sufficient conditions for the differenti al equation to have at most one cycle. A bound on the number of cycles on s urfaces of higher connectivity is given by similar conditions.