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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)
Resource Information
The item Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, by Leonid Shaikhet, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, by Leonid Shaikhet, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 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 continuoustime 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; • predatorprey 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
 Language
 eng
 Extent
 XII, 342 p. 157 illus., 28 illus. in color.
 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 PredatorPrey with Aftereffect and Stochastic Perturbations
 Stability of SIR Epidemic Model Equilibrium Points
 Stability of Some Social Mathematical Models with Delay by Stochastic Perturbations
 Isbn
 9783319001012
 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
 Subject

 Probability Theory and Stochastic Processes
 Engineering
 Functional equations
 Vibration, Dynamical Systems, Control
 Functional equations
 Mathematical optimization
 Mathematical optimization
 Distribution (Probability theory)
 Distribution (Probability theory)
 Vibration
 Statistical Physics, Dynamical Systems and Complexity
 Vibration
 Electronic resources
 Vibration
 Engineering
 Functional equations
 Engineering
 Mathematical optimization
 Distribution (Probability theory)
 Calculus of Variations and Optimal Control; Optimization
 Difference and Functional Equations
 Control
 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 continuoustime 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; • predatorprey 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
 TJ212225
 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)
 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 PredatorPrey 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
 10.1007/9783319001012
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319001012
 Label
 Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, by Leonid Shaikhet, (electronic resource)
 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 PredatorPrey 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
 10.1007/9783319001012
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319001012
Subject
 Calculus of Variations and Optimal Control; Optimization
 Control
 Difference and Functional Equations
 Distribution (Probability theory)
 Distribution (Probability theory)
 Distribution (Probability theory)
 Electronic resources
 Engineering
 Engineering
 Engineering
 Functional equations
 Functional equations
 Functional equations
 Mathematical optimization
 Mathematical optimization
 Mathematical optimization
 Probability Theory and Stochastic Processes
 Statistical Physics, Dynamical Systems and Complexity
 Vibration
 Vibration
 Vibration
 Vibration, Dynamical Systems, Control
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/LyapunovFunctionalsandStabilityofStochastic/wtTPyJeawzU/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/LyapunovFunctionalsandStabilityofStochastic/wtTPyJeawzU/">Lyapunov Functionals and Stability of Stochastic Functional Differential Equations, by Leonid Shaikhet, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>