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Explicit periodic solutions in a model of a relay controller with delay and forcing

Explicit periodic solutions in a model of a relay controller with delay and forcing
Explicit periodic solutions in a model of a relay controller with delay and forcing
In this paper we use a combination of numerical and analytical methods to find and construct solutions of a cameo model of relay control, formulated as a piecewise-constant delay differential equation (DDE). Numerical solutions of a related equation, where the discontinuities of the original DDE are smoothed out, are used to guide the construction of explicit solutions of the original DDE. On the other hand, the construction of explicit solutions provides starting data for numerical continuation of the smoothed equation. The stability of the explicit solutions can also be inferred from the numerical approach
0951-7715
2637-2656
Barton, David A.W.
3003bb1f-d648-4d00-a309-8ab75f333df0
Krauskopf, Bernd
a4fa8a40-8801-45d6-bb33-97f25ee166f1
Wilson, R. Eddie
01d7f1f2-f8ee-4661-b713-dcefcddb89bd
Barton, David A.W.
3003bb1f-d648-4d00-a309-8ab75f333df0
Krauskopf, Bernd
a4fa8a40-8801-45d6-bb33-97f25ee166f1
Wilson, R. Eddie
01d7f1f2-f8ee-4661-b713-dcefcddb89bd

Barton, David A.W., Krauskopf, Bernd and Wilson, R. Eddie (2005) Explicit periodic solutions in a model of a relay controller with delay and forcing. Nonlinearity, 18 (6), 2637-2656. (doi:10.1088/0951-7715/18/6/012).

Record type: Article

Abstract

In this paper we use a combination of numerical and analytical methods to find and construct solutions of a cameo model of relay control, formulated as a piecewise-constant delay differential equation (DDE). Numerical solutions of a related equation, where the discontinuities of the original DDE are smoothed out, are used to guide the construction of explicit solutions of the original DDE. On the other hand, the construction of explicit solutions provides starting data for numerical continuation of the smoothed equation. The stability of the explicit solutions can also be inferred from the numerical approach

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Published date: November 2005

Identifiers

Local EPrints ID: 184261
URI: http://eprints.soton.ac.uk/id/eprint/184261
ISSN: 0951-7715
PURE UUID: 5a192f70-d8c8-484f-8276-52f6ef56abce

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Date deposited: 19 May 2011 08:42
Last modified: 16 Jul 2019 23:40

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