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Stability criteria for differential equations with variable time delays

Record type: Article

Time delays are an important aspect of mathematical modelling, but often result in highly complicated equations which are difficult to treat analytically. In this paper it is shown how careful application of certain undergraduate tools such as the Method of Steps and the Principle of the Argument can yield significant results. Certain delay differential equations arising in population dynamics may serve as good teaching examples for these methods. The determination of linear stability properties for an ordinary differential equation with a varying time delay is carried out through discrete point analysis, either by seeking explicit solutions or leading to the consideration of a difference equation and the roots of a characteristic polynomial. Numerical simulations carried out using MATLAB Simulink are compared to the analytical solutions, and computation is also used to suggest extensions to some results.

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Citation

Schley, D., Shail, R. and Gourley, S.A. (2002) Stability criteria for differential equations with variable time delays International Journal of Mathematical Education in Science and Technology, 33, (3), pp. 359-375. (doi:10.1080/00207390110118980).

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Published date: 2002

Identifiers

Local EPrints ID: 29285
URI: http://eprints.soton.ac.uk/id/eprint/29285
ISSN: 0020-739X
PURE UUID: 9e82e7ff-4acf-47ea-a83d-a9723fff6ffb

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Date deposited: 12 May 2006
Last modified: 17 Jul 2017 15:58

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Contributors

Author: D. Schley
Author: R. Shail
Author: S.A. Gourley

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