000			04173nam a22005055i 4500
001			978-3-319-00101-2
003			DE-He213
005			20170628034020.0
007			cr nn 008mamaa
008			130330s2013 gw | s |||| 0|eng d
020			_a9783319001012 _9978-3-319-00101-2
024	7		_a10.1007/978-3-319-00101-2 _2doi
050		4	_aTJ212-225
072		7	_aTJFM _2bicssc
072		7	_aTEC004000 _2bisacsh
082	0	4	_a629.8 _223
100	1		_aShaikhet, Leonid. _eauthor.
245	1	0	_aLyapunov Functionals and Stability of Stochastic Functional Differential Equations _h[electronic resource] / _cby Leonid Shaikhet.
264		1	_aHeidelberg : _bSpringer International Publishing : _bImprint: Springer, _c2013.
300			_aXII, 342 p. 157 illus., 28 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_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.
520			_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.
650		0	_aEngineering.
650		0	_aFunctional equations.
650		0	_aMathematical optimization.
650		0	_aDistribution (Probability theory).
650		0	_aVibration.
650	1	4	_aEngineering.
650	2	4	_aControl.
650	2	4	_aDifference and Functional Equations.
650	2	4	_aStatistical Physics, Dynamical Systems and Complexity.
650	2	4	_aCalculus of Variations and Optimal Control; Optimization.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aVibration, Dynamical Systems, Control.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783319001005
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-319-00101-2
912			_aZDB-2-ENG
999			_c17896 _d17896