Global asymptotic behavior for delay dynamic equations

We give conditions under which the trivial solution of a first-order nonlinear variable-delay dynamic equation is asymptotically stable, for arbitrary time scales that are unbounded above. In an example, we apply our techniques to a logistic dynamic equation on isolated, unbounded time scales.

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Bibliographic Details
Published in:Nonlinear analysis 2007-04, Vol.66 (7), p.1633-1644
Main Authors: Anderson, Douglas R., Kenz, Zackary R.
Format: Article
Language:English
Subjects:
Asymptotic behavior
Delay
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematics
Nonlinear equation
Sciences and techniques of general use
Time scales
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Description
Summary:We give conditions under which the trivial solution of a first-order nonlinear variable-delay dynamic equation is asymptotically stable, for arbitrary time scales that are unbounded above. In an example, we apply our techniques to a logistic dynamic equation on isolated, unbounded time scales.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2006.02.014