Franklin

Lyapunov functionals and stability of stochastic functional differential equations / Leonid Shaikhet.

Author/Creator:
Shaĭkhet, L. E. (Leonid Efimovich), author.
Publication:
Cham, Switzlerland : Springer, [2013]
Format/Description:
Book
xii, 342 pages : illustrations (some color) ; 24 cm
Subjects:
Lyapunov functions.
Stochastic differential equations.
Summary:
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 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 differenetial equations with constant and distributed delays. The proposed method is used for stability investigation of different mathematical models.
Contents:
Short Introduction to Stability Theory of Deterministic Functional Differential Equations
Stochastic Functional Differential Equations and Procedure of Constructing Lyapunov Functionals
Stability of Linear Scalar Equations
Stability of Linear Systems of Two Equations
Stability of Systems with Nonlinearities
Matrix Riccati Equations in Stability of Linear Stochastic Differential Equations with Delays
Stochastic Systems with Markovian Switching
Stabilization of the Controlled Inverted Pendulum by a Control with Delay
Stability of Equilibrium Points of Nicholson's Blowflies Equation with Stochastic Perturbations
Stability of Positive Equilibrium Point of Nonlinear System of Type of Predator-Prey with Aftereffect and Stochastic Perturbations
Stability of SIR Epidemic Model Equilibrium Points
Stability of Some Social Mathematical Models with Delay Under Stochastic Perturbations.
Notes:
Includes bibliographical references (pages 325-338) and index.
Local notes:
Acquired for the Penn Libraries with assistance from the Benjamin Franklin Library Fund.
Contributor:
Benjamin Franklin Library Fund.
ISBN:
3319001000
9783319001005
9783319001012 (ebook)
OCLC:
827083517
Publisher Number:
99955794296
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