Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

  • Leonid Shaikhet

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 discrete- and continuous-time difference equations.
The text begins with a description of the peculiarities of deterministic and stochastic functional differential equations. There follow basic definitions for stability theory of stochastic hereditary systems, and a 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.


General Method of Lyapunov Functionals Hereditary Systems Numerical Simulation Stability Theory Stochastic Differential Equations

Authors and affiliations

  • Leonid Shaikhet
    • 1
  1. 1.Department of Higher MathematicsDonetsk State University of ManagementDonetskUkraine

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2013
  • Publisher Name Springer, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-319-00100-5
  • Online ISBN 978-3-319-00101-2
  • Buy this book on publisher's site
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