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Titlebook: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations; Leonid Shaikhet Book 2013 Springer International Publi

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发表于 2025-3-21 19:39:42 | 显示全部楼层 |阅读模式
书目名称Lyapunov Functionals and Stability of Stochastic Functional Differential Equations
编辑Leonid Shaikhet
视频video
概述Detailed description of Lyapunov functional construction will allow researchers to analyse stability results for hereditary systems more easily.Profuse analytical and numerical examples help to explai
图书封面Titlebook: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations;  Leonid Shaikhet Book 2013 Springer International Publi
描述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 both a description and a delineation of the peculiarities of deterministic and stochastic functional differential equations. There follows basic definitions for stability theory of stochastic hereditary systems, and the 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 develo
出版日期Book 2013
关键词General Method of Lyapunov Functionals; Hereditary Systems; Numerical Simulation; Stability Theory; Stoc
版次1
doihttps://doi.org/10.1007/978-3-319-00101-2
isbn_softcover978-3-319-03352-5
isbn_ebook978-3-319-00101-2
copyrightSpringer International Publishing Switzerland 2013
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书目名称Lyapunov Functionals and Stability of Stochastic Functional Differential Equations网络公开度学科排名




书目名称Lyapunov Functionals and Stability of Stochastic Functional Differential Equations被引频次




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发表于 2025-3-21 22:20:54 | 显示全部楼层
Book 2013 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 Equat
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Stochastic Systems with Markovian Switching,articular, an application to Markov chain with two states and numerical simulation of systems with Markovian switching are considered. Some examples of using the proposed numerical procedure are considered. The results of the calculations are presented by 15 figures.
发表于 2025-3-22 14:07:35 | 显示全部楼层
,Stability of Positive Equilibrium Point of Nonlinear System of Type of Predator–Prey with Aftereffef the constructed linear system are at the same time sufficient conditions for the stability in probability of the positive equilibrium point of the initial nonlinear system under stochastic perturbations. The obtained stability regions are illustrated by six figures.
发表于 2025-3-22 20:59:57 | 显示全部楼层
Stabilization of the Controlled Inverted Pendulum by a Control with Delay,ns. Via the general method of construction of Lyapunov functionals sufficient conditions for stabilization of zero solution by stochastic perturbations are obtained, nonzero steady-state solutions are investigated. 38 figures show a behavior of the controlled inverted pendulum in the case of stable and unstable equilibrium.
发表于 2025-3-23 00:01:31 | 显示全部楼层
Stability of Some Social Mathematical Models with Delay Under Stochastic Perturbations,is applied also to the social obesity epidemic models with distributed delay. The obtained results are illustrated by four figures with numerical simulations of stability regions and trajectories of solutions.
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Stability of Systems with Nonlinearities,on of stability in probability for nonlinear systems with the level of nonlinearity higher than one can be reduced to investigation of asymptotic mean square stability of the linear part of the considered nonlinear system. The obtained results are illustrated by 18 figures.
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