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Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback.
- Source :
-
Dynamical Systems: An International Journal . Mar2011, Vol. 26 Issue 1, p85-101. 17p. 2 Graphs. - Publication Year :
- 2011
-
Abstract
- In many situations in physics, engineering and biology time delays arise naturally due to the time needed to transport information from one part of the system to another and/or to react to incoming information. When differential equations are used in the mathematical modelling, then incorporating time delays leads to a description by a delay differential equation. We consider here a class of second-order scalar delay equations without instantaneous feedback, where the delays enter according to a distribution function. This is a natural description whenever there is more than one delay. In this article we show that for this class of systems one can derive stability information about the distributed-delay system by considering the single-delay system where the delay is the mean delay of the distribution function. More specifically, we prove that the asymptotic stability of the zero solution of the second-order delay equation with symmetric delay distribution is implied by the stability of the associated mean-delay equation. Our proof is based on the comparison of stability charts of the two equations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14689367
- Volume :
- 26
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Dynamical Systems: An International Journal
- Publication Type :
- Academic Journal
- Accession number :
- 58089769
- Full Text :
- https://doi.org/10.1080/14689367.2010.523889