Stability Of Differential Equations With Aftereffect
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Introduction To The Theory Of Functional Differential Equations Methods And Applications
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Author : Nikolaj Viktorovič Azbelev
language : en
Publisher: Hindawi Publishing Corporation
Release Date : 2007
Introduction To The Theory Of Functional Differential Equations Methods And Applications written by Nikolaj Viktorovič Azbelev and has been published by Hindawi Publishing Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Electronic books categories.
Stability Of Functional Differential Equations
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Author :
language : en
Publisher: Elsevier
Release Date : 1986-04-15
Stability Of Functional Differential Equations written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-04-15 with Mathematics categories.
This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.
Qualitative Analysis Of Set Valued Differential Equations
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Author : Anatoly A. Martynyuk
language : en
Publisher: Springer
Release Date : 2019-04-02
Qualitative Analysis Of Set Valued Differential Equations written by Anatoly A. Martynyuk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-02 with Mathematics categories.
The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.
Nonoscillation Theory Of Functional Differential Equations With Applications
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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23
Nonoscillation Theory Of Functional Differential Equations With Applications written by Ravi P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-23 with Mathematics categories.
This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types, equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference material. Nonoscillation Theory of Functional Differential Equations with Applications is addressed to a wide audience of researchers in mathematics and practitioners.
Functional Equations With Causal Operators
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Author : C. Corduneanu
language : en
Publisher: CRC Press
Release Date : 2002-09-05
Functional Equations With Causal Operators written by C. Corduneanu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-05 with Mathematics categories.
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with cau
Stability Of Differential Equations With Aftereffect
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Author : N.V. Azbelev
language : en
Publisher: CRC Press
Release Date : 2002-10-03
Stability Of Differential Equations With Aftereffect written by N.V. Azbelev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-03 with Mathematics categories.
Stability of Differential Equations with Aftereffect presents stability theory for differential equations concentrating on functional differential equations with delay, integro-differential equations, and related topics. The authors provide background material on the modern theory of functional differential equations and introduce some new flexible methods for investigating the asymptotic behaviour of solutions to a range of equations. The treatment also includes some results from the authors' research group based at Perm and provides a useful reference text for graduates and researchers working in mathematical and engineering science.
Applied Theory Of Functional Differential Equations
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Author : V. Kolmanovskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applied Theory Of Functional Differential Equations written by V. Kolmanovskii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems). The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and stochastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8. For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.
Functional Differential Equations
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Author : Constantin Corduneanu
language : en
Publisher: John Wiley & Sons
Release Date : 2016-03-25
Functional Differential Equations written by Constantin Corduneanu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-25 with Mathematics categories.
Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations. The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features: • Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types • Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines • Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay • An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity • An extensive Bibliography with over 550 references that connects the presented concepts to further topical exploration Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes. CONSTANTIN CORDUNEANU, PhD, is Emeritus Professor in the Department of Mathematics at The University of Texas at Arlington, USA. The author of six books and over 200 journal articles, he is currently Associate Editor for seven journals; a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Romanian Academy; and past president of the American Romanian Academy of Arts and Sciences. YIZENG LI, PhD, is Professor in the Department of Mathematics at Tarrant County College, USA. He is a member of the Society for Industrial and Applied Mathematics. MEHRAN MAHDAVI, PhD, is Professor in the Department of Mathematics at Bowie State University, USA. The author of numerous journal articles, he is a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Mathematical Association of America.
Stability And Control Processes
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Author : Nikolay Smirnov
language : en
Publisher: Springer Nature
Release Date : 2022-03-15
Stability And Control Processes written by Nikolay Smirnov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-15 with Technology & Engineering categories.
The proceedings of the 4th Stability and Control Processes Conference are focused on modern applied mathematics, stability theory, and control processes. The conference was held in recognition of the 90th birthday of Professor Vladimir Ivanovich Zubov (1930–2000). This selection of papers reflects the wide-ranging nature of V. I. Zubov’s work, which included contributions to the development of the qualitative theory of differential equations, the theory of rigid body motion, optimal control theory, and the theory of electromagnetic fields. It helps to advance many aspects of the theory of control systems, including questions of motion stability, nonlinear oscillations in control systems, navigation and reliability of control devices, vibration theory, and quantization of orbits. The disparate applications covered by the book – in mechanical systems, game theory, solid-state physics, socio-economic systems and medical and biological systems, control automata and navigation – are developments from Professor Zubov’s in-depth studies on the theory of stability of motion, the theory of automatic control and the theory of the motions of optimal processes. Stability and Control Processes presents research continuing the legacy of V. I. Zubov and updates it with sections focused on intelligence-based control. These proceedings will be of interest to academics, professionals working in industry and researchers alike.
Lyapunov Functionals And Stability Of Stochastic Difference Equations
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Author : Leonid Shaikhet
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-02
Lyapunov Functionals And Stability Of Stochastic Difference Equations written by Leonid Shaikhet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-02 with Technology & Engineering categories.
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.