Development and application of Halanay-type theory: Evolutionary differential and difference equations with time lag

C. T H Baker

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We consider extensions, developments and modifications of a result due to Halanay, and the application of "Halanay-type inequalities" in the analysis and numerics of retarded functional-differential equations, difference equations, and retarded functional-difference equations. Our emphasis is on the variety, structure and development, and future development, of Halanay-type results and their applications. We classify and present novel results of Halanay type (linear and non-linear, discrete, semi-discrete, and continuous) and establish their relevance to delay-differential equations, discretized analogues (we consider θ-methods), and difference equations. A rôle for such results in stability and contractivity analysis is made apparent. © 2010 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)2663-2682
    Number of pages19
    JournalJournal of Computational and Applied Mathematics
    Volume234
    Issue number9
    DOIs
    Publication statusPublished - 1 Sept 2010

    Keywords

    • Applications
    • Deterministic & Itô delay equations
    • Difference/delay differential equations
    • Difference/differential inequalities with maxima
    • Generalizations of Halanay's lemma
    • Linear θ-methods

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