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

D.A.W. Barton, B. Krauskopf, R.E. Wilson

Research output: Contribution to JournalArticleAcademicpeer-review

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.
Original languageEnglish
Pages (from-to)2637-2656
Number of pages20
JournalNonlinearity
Volume18
Issue number6
Early online date16 Sep 2005
DOIs
Publication statusPublished - Nov 2005

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