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Lyapunov Functionals and Stability of Stochastic Functional Differential Equations pp 1–28Cite as

Short Introduction to Stability Theory of Deterministic Functional Differential Equations

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Abstract

Chapter 1 presents general classification and some peculiarities of functional differential equations; in particular, some examples are shown when a functional differential equation can be reduced to ordinary differential equation. Some properties of solutions of functional differential equations and the method of steps for a solution of a delay differential equation are discussed. It is shown how small delay in the equation can influence the stability of the solution. Characteristic equations for retarded differential equations and the Routh–Hurwitz stability conditions for systems without delay are described. This section covers some theoretical backgrounds of the differential equations used in the book with concentration on mathematical rigor. A lot of examples of numerical simulation of stability regions and solutions of the considered equations are illustrated by 31 figures.

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Authors and Affiliations

  1. Department of Higher Mathematics, Donetsk State University of Management, Donetsk, Ukraine

    Leonid Shaikhet

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  1. Leonid Shaikhet
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Shaikhet, L. (2013). Short Introduction to Stability Theory of Deterministic Functional Differential Equations. In: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00101-2_1

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  • DOI: https://doi.org/10.1007/978-3-319-00101-2_1

  • Publisher Name: Springer, Heidelberg

  • Print ISBN: 978-3-319-00100-5

  • Online ISBN: 978-3-319-00101-2

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