Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

Authors: Shaikhet, Leonid

  • Detailed description of Lyapunov functional construction will allow researchers to analyse stability results for hereditary systems more easily
  • Profuse analytical and numerical examples help to explain the methods used
  • Demonstrates a method that can be usefully applied in economic, mechanical, biological and ecological systems
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About this book

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for difference equations with discrete and continuous time. The text begins with both a description and a delineation of the peculiarities of deterministic and stochastic functional differential equations. There follows basic definitions for stability theory of stochastic hereditary systems, and the formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of different mathematical models such as: • inverted controlled pendulum; • Nicholson's blowflies equation; • predator-prey relationships; • epidemic development; and • mathematical models that describe human behaviours related to addictions and obesity. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations is primarily addressed to experts in stability theory but will also be of interest to professionals and students in pure and computational mathematics, physics, engineering, medicine, and biology.

Reviews

From the reviews:

 “This is a book entirely devoted to the stability of stochastic functional differential equations, including various stochastic delay differential equations. This book is well written by a true expert in the field. In addition to analysis, it contains many simulation results. This book should be beneficial to researchers both in mathematics and control areas and in various applied areas who need to use stability.” (Fuke Wu, Mathematical Reviews, January, 2014)


Table of contents (12 chapters)

  • Short Introduction to Stability Theory of Deterministic Functional Differential Equations

    Shaikhet, Leonid

    Pages 1-28

  • Stochastic Functional Differential Equations and Procedure of Constructing Lyapunov Functionals

    Shaikhet, Leonid

    Pages 29-52

  • Stability of Linear Scalar Equations

    Shaikhet, Leonid

    Pages 53-96

  • Stability of Linear Systems of Two Equations

    Shaikhet, Leonid

    Pages 97-111

  • Stability of Systems with Nonlinearities

    Shaikhet, Leonid

    Pages 113-152

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-319-00101-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-319-00100-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-319-03352-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Lyapunov Functionals and Stability of Stochastic Functional Differential Equations
Authors
Copyright
2013
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-00101-2
DOI
10.1007/978-3-319-00101-2
Hardcover ISBN
978-3-319-00100-5
Softcover ISBN
978-3-319-03352-5
Edition Number
1
Number of Pages
XII, 342
Topics