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Stability criteria for differential equations with variable time delays

Stability criteria for differential equations with variable time delays
Stability criteria for differential equations with variable time delays
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.
0020-739X
359-375
Schley, D.
3d807658-2cfd-40e6-90ba-5032f88bb54b
Shail, R.
efc58cdd-c38e-49ff-acc2-f2099f452554
Gourley, S.A.
1aa9c89e-dfca-43f6-ad4d-4ecbe379094c
Schley, D.
3d807658-2cfd-40e6-90ba-5032f88bb54b
Shail, R.
efc58cdd-c38e-49ff-acc2-f2099f452554
Gourley, S.A.
1aa9c89e-dfca-43f6-ad4d-4ecbe379094c

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), 359-375. (doi:10.1080/00207390110118980).

Record type: Article

Abstract

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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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: 07 Jan 2022 22:23

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Contributors

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

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