Lyapunov Functionals and Stability of Stochastic Difference Equations

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Wei, L. Anabtawi, M. Wang, C.


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    Hale, J. Springer, New York Download references. The authors would like to thank the reviewers for their constructive suggestions and helpful comments. The research was supported by the National Natural Science Foundation of China grant number Correspondence to Shuyong Li. The authors declare that there is no conflict of interest regarding the publication of this paper. The authors declare that they have no competing interests.

    Lyapunov Functionals and Stability of Stochastic Difference Equations

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    Abstract The main purpose of this paper is to investigate the convergence and stability of stochastic parabolic functional differential equations. Introduction In recent years, stochastic parabolic partial differential equations have received a great deal of attention due to their important applications in biological, control engineering, economics, physics, social sciences, and so on. Convergence analysis In this section, we utilize the comparison theorem in the context of Lyapunov-like function established in Sect.

    Introduction

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    Samenvatting 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.

    Stability of delay evolution equations with stochastic perturbations

    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. Examples are drawn from a variety of physical and biological systems including inverted pendulum control, Nicholson's blowflies equation and predator-prey relationships.

    Lyapunov Functionals and Stability of Stochastic Difference Equations is primarily addressed to experts in stability theory but will also be of use in the work of pure and computational mathematicians and researchers using the ideas of optimal control to study economic, mechanical and biological systems. Thus, its value will be appreciated even more by mathematicians and researchers in engineering and physics. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser.

    Engineering Control Engineering. Free Preview. 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 explain the methods used Demonstrates a method that can be usefully applied in economic, mechanical, biological and ecological systems see more benefits.

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