Lyapunov Functionals and Stability of Stochastic Difference 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

 

Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology. An important element in their study is their stability.

Stability conditions for difference equations with delay can be obtained using Lyapunov functionals.

Lyapunov Functionals and Stability of Stochastic Difference Equations describes the general method of Lyapunov functionals construction to investigate the stability of discrete- and continuous-time stochastic Volterra difference equations. The method allows the investigation of the degree to which the stability properties of differential equations are preserved in their difference analogues.

The text is self-contained, beginning with basic definitions and the mathematical fundamentals of Lyapunov functionals construction and moving on from particular to general stability results for stochastic difference equations with constant coefficients. Results are then discussed for stochastic difference equations of linear, nonlinear, delayed, discrete and continuous types. Examples are drawn from a variety of physical and biological systems including inverted pendulum control, Nicholson's blowflies equation and predator-prey relationships.

Lyapunov Functionals and Stability of Stochastic Difference Equations is primarily addressed to experts in stability theory but will also be of use in the work of pure and computational mathematicians and researchers using the ideas of optimal control to study economic, mechanical and biological systems.

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Reviews

From the reviews:

“This highly recommendable monograph is devoted to the qualitative study of stochastic difference equations with respect to boundedness and asymptotic stability. … the author cites numerous references, making the book a valuable contribution in the area of stochastic dynamical systems. … well written by a true expert in the field and achieves its goal of making the general idea of Lyapunov functionals more accessible to a larger audience. Thus, its value will be appreciated even more by mathematicians and researchers in engineering and physics.” (Henri Schurz, Mathematical Reviews, November, 2013)

“The book presents general method of construction of Lyapunov functionals for investigating stability of stochastic difference equations. … The book is primarily addressed to mathematicians, experts in stability theory, and professionals in control engineering.” (Zygmunt Hasiewicz, Zentralblatt MATH, Vol. 1255, 2013)

Table of contents (10 chapters)

  • Lyapunov-type Theorems and Procedure of Lyapunov Functionals Construction

    Shaikhet, Leonid

    Pages 1-10

  • Illustrative Example

    Shaikhet, Leonid

    Pages 11-21

  • Linear Equations with Stationary Coefficients

    Shaikhet, Leonid

    Pages 23-59

  • Linear Equations with Nonstationary Coefficients

    Shaikhet, Leonid

    Pages 61-77

  • Some Peculiarities of the Method

    Shaikhet, Leonid

    Pages 79-108

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-0-85729-685-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-0-85729-684-9
  • 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 Difference Equations
Authors
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-685-6
DOI
10.1007/978-0-85729-685-6
Hardcover ISBN
978-0-85729-684-9
Edition Number
1
Number of Pages
XII, 370
Topics