Authors:
- 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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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
Lyapunov Functionals and Stability of Stochastic Difference Equations describes a general method of Lyapunov functional 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 functional 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 systems including inverted pendulum control, study of epidemic development, 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.
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)Authors and Affiliations
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Department of Higher Mathematics, Donetsk State University of Management, Donetsk, Ukraine
Leonid Shaikhet
Bibliographic Information
Book Title: Lyapunov Functionals and Stability of Stochastic Difference Equations
Authors: Leonid Shaikhet
DOI: https://doi.org/10.1007/978-0-85729-685-6
Publisher: Springer London
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag London Limited 2011
Hardcover ISBN: 978-0-85729-684-9Published: 03 June 2011
Softcover ISBN: 978-1-4471-7166-9Published: 23 August 2016
eBook ISBN: 978-0-85729-685-6Published: 02 June 2011
Edition Number: 1
Number of Pages: XII, 370
Topics: Control and Systems Theory, Difference and Functional Equations, Calculus of Variations and Optimal Control; Optimization, Mathematical and Computational Biology, Probability Theory and Stochastic Processes, Vibration, Dynamical Systems, Control