The Resource Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, by Leonid Shaikhet, (electronic resource)

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, by Leonid Shaikhet, (electronic resource)

Label
Lyapunov Functionals and Stability of Stochastic Functional Differential Equations
Title
Lyapunov Functionals and Stability of Stochastic Functional Differential Equations
Statement of responsibility
by Leonid Shaikhet
Creator
Contributor
Author
Provider
Subject
Language
eng
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 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
http://library.link/vocab/creatorName
Shaikhet, Leonid
Image bit depth
0
LC call number
TJ212-225
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
http://library.link/vocab/subjectName
  • Engineering
  • Functional equations
  • Mathematical optimization
  • Distribution (Probability theory)
  • Vibration
  • Engineering
  • Control
  • Difference and Functional Equations
  • Statistical Physics, Dynamical Systems and Complexity
  • Calculus of Variations and Optimal Control; Optimization
  • Probability Theory and Stochastic Processes
  • Vibration, Dynamical Systems, Control
Label
Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, by Leonid Shaikhet, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Short Introduction to Stability Theory of Deterministic Functional Differential Equations -- 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 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 by Stochastic Perturbations
Dimensions
unknown
Extent
XII, 342 p. 157 illus., 28 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783319001012
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-00101-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-00101-2
Label
Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, by Leonid Shaikhet, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Short Introduction to Stability Theory of Deterministic Functional Differential Equations -- 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 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 by Stochastic Perturbations
Dimensions
unknown
Extent
XII, 342 p. 157 illus., 28 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783319001012
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-00101-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-00101-2

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