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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Diagonal dominance and harmless off-diagonal delays


Authors: Josef Hofbauer and Joseph W.-H. So
Journal: Proc. Amer. Math. Soc. 128 (2000), 2675-2682
MSC (1991): Primary 34K20
Published electronically: February 28, 2000
MathSciNet review: 1707519
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Abstract: Systems of linear differential equations with constant coefficients, as well as Lotka-Volterra equations, with delays in the off-diagonal terms are considered. Such systems are shown to be asymptotically stable for any choice of delays if and only if the matrix has a negative weakly dominant diagonal.


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Additional Information

Josef Hofbauer
Affiliation: Institut für Mathematik, Universität Wien, A-1090 Wien, Austria
Email: Josef.Hofbauer@univie.ac.at

Joseph W.-H. So
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: joseph.so@ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05564-7
PII: S 0002-9939(00)05564-7
Received by editor(s): October 23, 1998
Published electronically: February 28, 2000
Additional Notes: This research was partially supported by NSERC of Canada, grant number OGP36475.
Communicated by: Hal L. Smith
Article copyright: © Copyright 2000 American Mathematical Society