Overview
- 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
- Includes supplementary material: sn.pub/extras
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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.
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Keywords
Table of contents (12 chapters)
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Front Matter
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Back Matter
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)
Authors and Affiliations
Bibliographic Information
Book Title: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations
Authors: Leonid Shaikhet
DOI: https://doi.org/10.1007/978-3-319-00101-2
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing Switzerland 2013
Hardcover ISBN: 978-3-319-00100-5Published: 29 May 2013
Softcover ISBN: 978-3-319-03352-5Published: 23 June 2015
eBook ISBN: 978-3-319-00101-2Published: 29 March 2013
Edition Number: 1
Number of Pages: XII, 342
Topics: Control and Systems Theory, Difference and Functional Equations, Complex Systems, Calculus of Variations and Optimal Control; Optimization, Probability Theory and Stochastic Processes, Vibration, Dynamical Systems, Control