LEADER 05652nam 22008535 450 001 9910438050103321 005 20220406221646.0 010 $a3-319-00101-9 024 7 $a10.1007/978-3-319-00101-2 035 $a(CKB)2550000001045699 035 $a(EBL)1205641 035 $a(SSID)ssj0000879229 035 $a(PQKBManifestationID)11476055 035 $a(PQKBTitleCode)TC0000879229 035 $a(PQKBWorkID)10850373 035 $a(PQKB)11560647 035 $a(DE-He213)978-3-319-00101-2 035 $a(MiAaPQ)EBC1205641 035 $a(PPN)169137392 035 $a(EXLCZ)992550000001045699 100 $a20130330d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLyapunov functionals and stability of stochastic functional differential equations /$fby Leonid Shaikhet 205 $a1st ed. 2013. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2013. 215 $a1 online resource (342 p.) 300 $aDescription based upon print version of record. 311 $a3-319-03352-2 311 $a3-319-00100-0 320 $aIncludes bibliographical references and index. 327 $aShort 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. 330 $aStability 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. 606 $aControl engineering 606 $aDifference equations 606 $aFunctional equations 606 $aStatistical physics 606 $aDynamical systems 606 $aCalculus of variations 606 $aProbabilities 606 $aVibration 606 $aDynamics 606 $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aVibration, Dynamical Systems, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/T15036 615 0$aControl engineering. 615 0$aDifference equations. 615 0$aFunctional equations. 615 0$aStatistical physics. 615 0$aDynamical systems. 615 0$aCalculus of variations. 615 0$aProbabilities. 615 0$aVibration. 615 0$aDynamics. 615 14$aControl and Systems Theory. 615 24$aDifference and Functional Equations. 615 24$aComplex Systems. 615 24$aCalculus of Variations and Optimal Control; Optimization. 615 24$aProbability Theory and Stochastic Processes. 615 24$aVibration, Dynamical Systems, Control. 676 $a515.35 676 $a515.392 676 $a515/.35 700 $aShaikhet$b Leonid$4aut$4http://id.loc.gov/vocabulary/relators/aut$0720644 906 $aBOOK 912 $a9910438050103321 996 $aLyapunov Functionals and Stability of Stochastic Functional Differential Equations$92540126 997 $aUNINA