Lyapunov Functionals And Stability Of Stochastic Difference Equations

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Lyapunov Functionals and Stability of Stochastic Difference Equations

Author : Leonid Shaikhet
Publisher : Springer Science & Business Media
ISBN 13 : 085729685X
Total Pages : 374 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Lyapunov Functionals and Stability of Stochastic Difference Equations by : Leonid Shaikhet

Download or read book Lyapunov Functionals and Stability of Stochastic Difference Equations written by Leonid Shaikhet and published by Springer Science & Business Media. This book was released on 2011-06-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology. An important element in their study is their stability. Stability conditions for difference equations with delay can be obtained using a Lyapunov functional. Lyapunov Functionals and Stability of Stochastic Difference Equations describes a general method of Lyapunov functional construction to investigate the stability of discrete- and continuous-time stochastic Volterra difference equations. The method allows the investigation of the degree to which the stability properties of differential equations are preserved in their difference analogues. The text is self-contained, beginning with basic definitions and the mathematical fundamentals of Lyapunov functional construction and moving on from particular to general stability results for stochastic difference equations with constant coefficients. Results are then discussed for stochastic difference equations of linear, nonlinear, delayed, discrete and continuous types. Examples are drawn from a variety of physical systems including inverted pendulum control, study of epidemic development, 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.

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

Author : Leonid Shaikhet
Publisher : Springer Science & Business Media
ISBN 13 : 3319001019
Total Pages : 352 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Lyapunov Functionals and Stability of Stochastic Functional Differential Equations by : Leonid Shaikhet

Download or read book Lyapunov Functionals and Stability of Stochastic Functional Differential Equations written by Leonid Shaikhet and published by Springer Science & Business Media. This book was released on 2013-03-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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.

Dynamical Systems and Applications

Author : Ravi P. Agarwal
Publisher : World Scientific
ISBN 13 : 9789810223830
Total Pages : 720 pages
Book Rating : 4.2/5 (238 download)

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Book Synopsis Dynamical Systems and Applications by : Ravi P. Agarwal

Download or read book Dynamical Systems and Applications written by Ravi P. Agarwal and published by World Scientific. This book was released on 1995 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: World Scientific series in Applicable Analysis (WSSIAA) aims at reporting new developments of high mathematical standard and current interest. Each volume in the series shall be devoted to the mathematical analysis that has been applied or potentially applicable to the solutions of scientific, engineering, and social problems. For the past twenty five years, there has been an explosion of interest in the study of nonlinear dynamical systems. Mathematical techniques developed during this period have been applied to important nonlinear problems ranging from physics and chemistry to ecology and economics. All these developments have made dynamical systems theory an important and attractive branch of mathematics to scientists in many disciplines. This rich mathematical subject has been partially represented in this collection of 45 papers by some of the leading researchers in the area. This volume contains 45 state-of-art articles on the mathematical theory of dynamical systems by leading researchers. It is hoped that this collection will lead new direction in this field.Contributors: B Abraham-Shrauner, V Afraimovich, N U Ahmed, B Aulbach, E J Avila-Vales, F Battelli, J M Blazquez, L Block, T A Burton, R S Cantrell, C Y Chan, P Collet, R Cushman, M Denker, F N Diacu, Y H Ding, N S A El-Sharif, J E Fornaess, M Frankel, R Galeeva, A Galves, V Gershkovich, M Girardi, L Gotusso, J Graczyk, Y Hino, I Hoveijn, V Hutson, P B Kahn, J Kato, J Keesling, S Keras, V Kolmanovskii, N V Minh, V Mioc, K Mischaikow, M Misiurewicz, J W Mooney, M E Muldoon, S Murakami, M Muraskin, A D Myshkis, F Neuman, J C Newby, Y Nishiura, Z Nitecki, M Ohta, G Osipenko, N Ozalp, M Pollicott, Min Qu, Donal O-Regan, E Romanenko, V Roytburd, L Shaikhet, J Shidawara, N Sibony, W-H Steeb, C Stoica, G Swiatek, T Takaishi, N D Thai Son, R Triggiani, A E Tuma, E H Twizell, M Urbanski; T D Van, A Vanderbauwhede, A Veneziani, G Vickers, X Xiang, T Young, Y Zarmi.

Stochastic Functional Differential Equations

Author : S. E. A. Mohammed
Publisher : Pitman Advanced Publishing Program
ISBN 13 :
Total Pages : 268 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Stochastic Functional Differential Equations by : S. E. A. Mohammed

Download or read book Stochastic Functional Differential Equations written by S. E. A. Mohammed and published by Pitman Advanced Publishing Program. This book was released on 1984 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Random Dynamical Systems

Author : Ludwig Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 3662128780
Total Pages : 590 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Random Dynamical Systems by : Ludwig Arnold

Download or read book Random Dynamical Systems written by Ludwig Arnold and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.

Applied Stochastic Differential Equations

Author : Simo Särkkä
Publisher : Cambridge University Press
ISBN 13 : 1316510085
Total Pages : 327 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä

Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Advances in Discrete Dynamical Systems, Difference Equations and Applications

Author : Saber Elaydi
Publisher : Springer Nature
ISBN 13 : 303125225X
Total Pages : 534 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Advances in Discrete Dynamical Systems, Difference Equations and Applications by : Saber Elaydi

Download or read book Advances in Discrete Dynamical Systems, Difference Equations and Applications written by Saber Elaydi and published by Springer Nature. This book was released on 2023-03-25 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021. The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines. The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.

Optimal Control of Stochastic Difference Volterra Equations

Author : Leonid Shaikhet
Publisher : Springer
ISBN 13 : 3319132393
Total Pages : 224 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Optimal Control of Stochastic Difference Volterra Equations by : Leonid Shaikhet

Download or read book Optimal Control of Stochastic Difference Volterra Equations written by Leonid Shaikhet and published by Springer. This book was released on 2014-11-27 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equations commences with an historical introduction to the emergence of this type of equation with some additional mathematical preliminaries. It then deals with the necessary conditions for optimality in the control of the equations and constructs a feedback control scheme. The approximation of stochastic quasilinear Volterra equations with quadratic performance functionals is then considered. Optimal stabilization is discussed and the filtering problem formulated. Finally, two methods of solving the optimal control problem for partly observable linear stochastic processes, also with quadratic performance functionals, are developed. Integrating the author’s own research within the context of the current state-of-the-art of research in difference equations, hereditary systems theory and optimal control, this book is addressed to specialists in mathematical optimal control theory and to graduate students in pure and applied mathematics and control engineering.

Stochastic Stability of Differential Equations

Author : Rafail Khasminskii
Publisher : Springer Science & Business Media
ISBN 13 : 3642232809
Total Pages : 353 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Stochastic Stability of Differential Equations by : Rafail Khasminskii

Download or read book Stochastic Stability of Differential Equations written by Rafail Khasminskii and published by Springer Science & Business Media. This book was released on 2011-09-20 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of the present volume in 1980, the stochastic stability of differential equations has become a very popular subject of research in mathematics and engineering. To date exact formulas for the Lyapunov exponent, the criteria for the moment and almost sure stability, and for the existence of stationary and periodic solutions of stochastic differential equations have been widely used in the literature. In this updated volume readers will find important new results on the moment Lyapunov exponent, stability index and some other fields, obtained after publication of the first edition, and a significantly expanded bibliography. This volume provides a solid foundation for students in graduate courses in mathematics and its applications. It is also useful for those researchers who would like to learn more about this subject, to start their research in this area or to study the properties of concrete mechanical systems subjected to random perturbations.

Advances in Time-Delay Systems

Author : Silviu-Iulian Niculescu
Publisher : Springer Science & Business Media
ISBN 13 : 3642184820
Total Pages : 445 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Advances in Time-Delay Systems by : Silviu-Iulian Niculescu

Download or read book Advances in Time-Delay Systems written by Silviu-Iulian Niculescu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the mathematical description of a physical or biological process, it is a common practice \0 assume that the future behavior of Ihe process considered depends only on the present slate, and therefore can be described by a finite sct of ordinary diffe rential equations. This is satisfactory for a large class of practical systems. However. the existence of lime-delay elements, such as material or infonnation transport, of tcn renders such description unsatisfactory in accounting for important behaviors of many practical systems. Indeed. due largely to the current lack of effective metho dology for analysis and control design for such systems, the lime-delay elements arc often either neglected or poorly approximated, which frequently results in analysis and simulation of insufficient accuracy, which in turns leads to poor performance of the systems designed. Indeed, it has been demonstrated in the area of automatic control that a relatively small delay may lead to instability or significantly deteriora ted perfonnances for the corresponding closed-loop systems.

Practical Stability of Nonlinear Systems

Author : V. Lakshmikantham
Publisher : World Scientific
ISBN 13 : 9789810203566
Total Pages : 228 pages
Book Rating : 4.2/5 (35 download)

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Book Synopsis Practical Stability of Nonlinear Systems by : V. Lakshmikantham

Download or read book Practical Stability of Nonlinear Systems written by V. Lakshmikantham and published by World Scientific. This book was released on 1990 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book that deals with practical stability and its development. It presents a systematic study of the theory of practical stability in terms of two different measures and arbitrary sets and demonstrates the manifestations of general Lyapunov's method by showing how this effective technique can be adapted to investigate various apparently diverse nonlinear problems including control systems and multivalued differential equations.

Finite-Time Stability: An Input-Output Approach

Author : Francesco Amato
Publisher : John Wiley & Sons
ISBN 13 : 1119140528
Total Pages : 184 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Finite-Time Stability: An Input-Output Approach by : Francesco Amato

Download or read book Finite-Time Stability: An Input-Output Approach written by Francesco Amato and published by John Wiley & Sons. This book was released on 2018-10-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustness The interest in finite-time control has continuously grown in the last fifteen years. This book systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, with specific reference to linear time-varying systems and hybrid systems. It discusses analysis, design and robustness issues, and includes applications to real world engineering problems. While classical FTS has an important theoretical significance, IO-FTS is a more practical concept, which is more suitable for real engineering applications, the goal of the research on this topic in the coming years. Key features: Includes applications to real world engineering problems. Input-output finite-time stability (IO-FTS) is a practical concept, useful to study the behavior of a dynamical system within a finite interval of time. Computationally tractable conditions are provided that render the technique applicable to time-invariant as well as time varying and impulsive (i.e. switching) systems. The LMIs formulation allows mixing the IO-FTS approach with existing control techniques (e. g. H∞ control, optimal control, pole placement, etc.). This book is essential reading for university researchers as well as post-graduate engineers practicing in the field of robust process control in research centers and industries. Topics dealt with in the book could also be taught at the level of advanced control courses for graduate students in the department of electrical and computer engineering, mechanical engineering, aeronautics and astronautics, and applied mathematics.

Probabilistic Analysis and Related Topics

Author : A. T. Bharucha-Reid
Publisher : Elsevier
ISBN 13 : 1483275469
Total Pages : 271 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Probabilistic Analysis and Related Topics by : A. T. Bharucha-Reid

Download or read book Probabilistic Analysis and Related Topics written by A. T. Bharucha-Reid and published by Elsevier. This book was released on 2014-05-10 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic Analysis and Related Topics, Volume 3 focuses on the continuity, integrability, and differentiability of random functions, including operator theory, measure theory, and functional and numerical analysis. The selection first offers information on the qualitative theory of stochastic systems and Langevin equations with multiplicative noise. Discussions focus on phase-space evolution via direct integration, phase-space evolution, linear and nonlinear systems, linearization, and generalizations. The text then ponders on the stability theory of stochastic difference systems and Markov properties for random fields. Topics include Markov property of solutions of stochastic partial differential equations; Markov property for generalized Gaussian random fields; Markov properties for generalized random fields; stochastic stability of nonlinear systems; and linear stochastic systems. The publication examines the method of random contractors and its applications to random nonlinear equations, including integral contractors and applications to random equations; random contractors with random nonlinear majorant functions; and random contractors and application to random nonlinear operator equations. The selection is a valuable reference for mathematicians and researchers interested in the general theory of random functions.

Stability Analysis of Impulsive Functional Differential Equations

Author : Ivanka Stamova
Publisher : Walter de Gruyter
ISBN 13 : 3110221810
Total Pages : 241 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Stability Analysis of Impulsive Functional Differential Equations by : Ivanka Stamova

Download or read book Stability Analysis of Impulsive Functional Differential Equations written by Ivanka Stamova and published by Walter de Gruyter. This book was released on 2009 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Stability of Infinite Dimensional Stochastic Differential Equations with Applications

Author : Kai Liu
Publisher : CRC Press
ISBN 13 : 1420034820
Total Pages : 311 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Stability of Infinite Dimensional Stochastic Differential Equations with Applications by : Kai Liu

Download or read book Stability of Infinite Dimensional Stochastic Differential Equations with Applications written by Kai Liu and published by CRC Press. This book was released on 2005-08-23 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ

Recent Advances in Delay Differential and Difference Equations

Author : Ferenc Hartung
Publisher : Springer
ISBN 13 : 3319082515
Total Pages : 271 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Recent Advances in Delay Differential and Difference Equations by : Ferenc Hartung

Download or read book Recent Advances in Delay Differential and Difference Equations written by Ferenc Hartung and published by Springer. This book was released on 2014-08-22 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic and oscillatory properties of the solutions; stability theory; numerical approximations; and applications to real world phenomena using deterministic and stochastic discrete and continuous dynamical systems.

Stochastic Differential Equations with Markovian Switching

Author : Xuerong Mao
Publisher : Imperial College Press
ISBN 13 : 1860947018
Total Pages : 430 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Stochastic Differential Equations with Markovian Switching by : Xuerong Mao

Download or read book Stochastic Differential Equations with Markovian Switching written by Xuerong Mao and published by Imperial College Press. This book was released on 2006 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides the first systematic presentation of the theory of stochastic differential equations with Markovian switching. It presents the basic principles at an introductory level but emphasizes current advanced level research trends. The material takes into account all the features of Ito equations, Markovian switching, interval systems and time-lag. The theory developed is applicable in different and complicated situations in many branches of science and industry.