On the discretization of a delay differential equation

Authors
Cooke, KL Ivanov, AF
Citation
Kl. Cooke et Af. Ivanov, On the discretization of a delay differential equation, J DIF EQ AP, 6(1), 2000, pp. 105-119
Citations number
18
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
ISSN journal
10236198 → ACNP
Volume
6
Issue
1
Year of publication
2000
Pages
105 - 119
Database
ISI
SICI code
1023-6198(2000)6:1<105:OTDOAD>2.0.ZU;2-8
Abstract
The dynamics of the delay difference equation mu[Delta x(n) + alpha Delta x (n-N)] = -x(n+1) + f(x(n-N)) as n --> infinity is studied for small positiv e mu. The equation is shown to possess stable periodic solutions that corre spond to hyperbolic attracting cycles of the one-dimensional map f.