Stability Periodicity And Boundedness In Functional Dynamical Systems On Time Scales

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Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales

Author : Murat Adıvar
Publisher : Springer Nature
ISBN 13 : 3030421171
Total Pages : 416 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales by : Murat Adıvar

Download or read book Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales written by Murat Adıvar and published by Springer Nature. This book was released on 2020-04-23 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by recent increased activity of research on time scales, the book provides a systematic approach to the study of the qualitative theory of boundedness, periodicity and stability of Volterra integro-dynamic equations on time scales. Researchers and graduate students who are interested in the method of Lyapunov functions/functionals, in the study of boundedness of solutions, in the stability of the zero solution, or in the existence of periodic solutions should be able to use this book as a primary reference and as a resource of latest findings. This book contains many open problems and should be of great benefit to those who are pursuing research in dynamical systems or in Volterra integro-dynamic equations on time scales with or without delays. Great efforts were made to present rigorous and detailed proofs of theorems. The book should serve as an encyclopedia on the construction of Lyapunov functionals in analyzing solutions of dynamical systems on time scales. The book is suitable for a graduate course in the format of graduate seminars or as special topics course on dynamical systems. The book should be of interest to investigators in biology, chemistry, economics, engineering, mathematics and physics.

Advanced Differential Equations

Author : Youssef N. Raffoul
Publisher : Academic Press
ISBN 13 : 0323992811
Total Pages : 366 pages
Book Rating : 4.3/5 (239 download)

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Book Synopsis Advanced Differential Equations by : Youssef N. Raffoul

Download or read book Advanced Differential Equations written by Youssef N. Raffoul and published by Academic Press. This book was released on 2022-04-13 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Differential Equations provides coverage of high-level topics in ordinary differential equations and dynamical systems. The book delivers difficult material in an accessible manner, utilizing easier, friendlier notations and multiple examples. Sections focus on standard topics such as existence and uniqueness for scalar and systems of differential equations, the dynamics of systems, including stability, with examples and an examination of the eigenvalues of an accompanying linear matrix, as well as coverage of existing literature. From the eigenvalues' approach, to coverage of the Lyapunov direct method, this book readily supports the study of stable and unstable manifolds and bifurcations. Additional sections cover the study of delay differential equations, extending from ordinary differential equations through the extension of Lyapunov functions to Lyapunov functionals. In this final section, the text explores fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations. Includes content from a class-tested over multiple years with advanced undergraduate and graduate courses Presents difficult material in an accessible manner by utilizing easier, friendlier notations, multiple examples and thoughtful exercises of increasing difficulty Provides content that is appropriate for advanced classes up to, and including, a two-semester graduate course in exploring the theory and applications of ordinary differential equations Requires minimal background in real analysis and differential equations Offers a partial solutions manual for student study

Stability of Dynamical Systems

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 0817644865
Total Pages : 516 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Stability of Dynamical Systems by :

Download or read book Stability of Dynamical Systems written by and published by Springer Science & Business Media. This book was released on 2008 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.

Advances in Difference Equations and Discrete Dynamical Systems

Author : Saber Elaydi
Publisher : Springer
ISBN 13 : 9811064091
Total Pages : 282 pages
Book Rating : 4.8/5 (11 download)

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

Download or read book Advances in Difference Equations and Discrete Dynamical Systems written by Saber Elaydi and published by Springer. This book was released on 2017-11-13 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 22nd International Conference on Difference Equations and Applications, held at Osaka Prefecture University, Osaka, Japan, in July 2016. The conference brought together both experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete dynamical systems with applications to mathematical sciences and, in particular, mathematical biology and economics. This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete dynamical systems, and their applications.

Difference Equations, Discrete Dynamical Systems and Applications

Author : Saber Elaydi
Publisher : Springer
ISBN 13 : 3030200167
Total Pages : 382 pages
Book Rating : 4.0/5 (32 download)

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

Download or read book Difference Equations, Discrete Dynamical Systems and Applications written by Saber Elaydi and published by Springer. This book was released on 2019-06-29 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the proceedings of the 23rd International Conference on Difference Equations and Applications, ICDEA 2017, held at the West University of Timișoara, Romania, under the auspices of the International Society of Difference Equations (ISDE), July 24 - 28, 2017. It includes new and significant contributions in the field of difference equations, discrete dynamical systems and their applications in various sciences. Disseminating recent studies and related results and promoting advances, the book appeals to PhD students, researchers, educators and practitioners in the field.

Topics on Stability and Periodicity in Abstract Differential Equations

Author : James Hetao Liu
Publisher : World Scientific
ISBN 13 : 9812818235
Total Pages : 219 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Topics on Stability and Periodicity in Abstract Differential Equations by : James Hetao Liu

Download or read book Topics on Stability and Periodicity in Abstract Differential Equations written by James Hetao Liu and published by World Scientific. This book was released on 2008 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent methods of study on the asymptotic behavior of solutions of abstract differential equations such as stability, exponential dichotomy, periodicity, almost periodicity, and almost automorphy of solutions. The chosen methods are described in a way that is suitable to those who have some experience with ordinary differential equations. The book is intended for graduate students and researchers in the related areas.

Stability of Dynamical Systems

Author : Xiaoxin Liao
Publisher : Elsevier
ISBN 13 : 0080550614
Total Pages : 719 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Stability of Dynamical Systems by : Xiaoxin Liao

Download or read book Stability of Dynamical Systems written by Xiaoxin Liao and published by Elsevier. This book was released on 2007-08-01 with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems. Presents comprehensive theory and methodology of stability analysis Can be used as textbook for graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, scientific computation Serves as a comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers

Stability and Stable Oscillations in Discrete Time Systems

Author : Aristide Halanay
Publisher : CRC Press
ISBN 13 : 9789056996710
Total Pages : 310 pages
Book Rating : 4.9/5 (967 download)

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Book Synopsis Stability and Stable Oscillations in Discrete Time Systems by : Aristide Halanay

Download or read book Stability and Stable Oscillations in Discrete Time Systems written by Aristide Halanay and published by CRC Press. This book was released on 2000-10-31 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The expertise of a professional mathmatician and a theoretical engineer provides a fresh perspective of stability and stable oscillations. The current state of affairs in stability theory, absolute stability of control systems, and stable oscillations of both periodic and almost periodic discrete systems is presented, including many applications in engineering such as stability of digital filters, digitally controlled thermal processes, neurodynamics, and chemical kinetics. This book will be an invaluable reference source for those whose work is in the area of discrete dynamical systems, difference equations, and control theory or applied areas that use discrete time models.

Functional Dynamic Equations on Time Scales

Author : Svetlin G. Georgiev
Publisher : Springer
ISBN 13 : 3030154203
Total Pages : 885 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Functional Dynamic Equations on Time Scales by : Svetlin G. Georgiev

Download or read book Functional Dynamic Equations on Time Scales written by Svetlin G. Georgiev and published by Springer. This book was released on 2019-05-03 with total page 885 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.

Dynamic Calculus and Equations on Time Scales

Author : Svetlin G. Georgiev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111182975
Total Pages : 336 pages
Book Rating : 4.1/5 (111 download)

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Book Synopsis Dynamic Calculus and Equations on Time Scales by : Svetlin G. Georgiev

Download or read book Dynamic Calculus and Equations on Time Scales written by Svetlin G. Georgiev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-09-18 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest advancements in time scale calculus are the focus of this book. New types of time-scale integral transforms are discussed in the book, along with how they can be used to solve dynamic equations. Novel numerical techniques for partial dynamic equations on time scales are described. New time scale inequalities for exponentially convex functions are introduced as well.

Selected Topics in Almost Periodicity

Author : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110763524
Total Pages : 734 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Selected Topics in Almost Periodicity by : Marko Kostić

Download or read book Selected Topics in Almost Periodicity written by Marko Kostić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.

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.

Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions

Author : T. Yoshizawa
Publisher : Springer Science & Business Media
ISBN 13 : 146126376X
Total Pages : 240 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions by : T. Yoshizawa

Download or read book Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions written by T. Yoshizawa and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since there are several excellent books on stability theory, the author selected some recent topics in stability theory which are related to existence theorems for periodic solutions and for almost periodic solutions. The author hopes that these notes will also serve as an introduction to stability theory. These notes contain stability theory by Liapunov's second method and somewhat extended discussion of stability properties in almost periodic systems, and the existence of a periodic solution in a periodic system is discussed in connection with the boundedness of solutions, and the existence of an almost periodic solution in an almost periodic system is considered in con nection with some stability property of a bounded solution. In the theory of almost periodic systems, one has to consider almost periodic functions depending on parameters, but most of text books on almost periodic functions do not contain this case. Therefore, as mathemati cal preliminaries, the first chapter is intended to provide a guide for some properties of almost periodic functions with parameters as well as for properties of asymptotically almost periodic functions. These notes originate from a seminar on stability theory given by the author at the Mathematics Department of Michigan State Univer sity during the academic year 1972-1973. The author is very grateful to Professor Pui-Kei Wong and members of the Department for their warm hospitality and many helpful conversations. The author wishes to thank Mrs.

Almost Periodicity, Chaos, and Asymptotic Equivalence

Author : Marat Akhmet
Publisher : Springer
ISBN 13 : 303020572X
Total Pages : 360 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Almost Periodicity, Chaos, and Asymptotic Equivalence by : Marat Akhmet

Download or read book Almost Periodicity, Chaos, and Asymptotic Equivalence written by Marat Akhmet and published by Springer. This book was released on 2019-06-20 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis. Prof. Akhmet's lucid and rigorous examination proves these oscillations are a "regular" component of chaotic attractors. The book focuses on almost periodic functions, first of all, as Stable (asymptotically) solutions of differential equations of different types, presumably discontinuous; and, secondly, as non-isolated oscillations in chaotic sets. Finally, the author proves the existence of Almost Periodic Oscillations (asymptotic and bi-asymptotic) by asymptotic equivalence between systems. The book brings readers' attention to contemporary methods for considering oscillations as well as to methods with strong potential for study of chaos in the future. Providing three powerful instruments for mathematical research of oscillations where dynamics are observable and applied, the book is ideal for engineers as well as specialists in electronics, computer sciences, robotics, neural networks, artificial networks, and biology. Distinctively combines results and methods of the theory of differential equations with thorough investigation of chaotic dynamics with almost periodic ingredients; Provides all necessary mathematical basics in their most developed form, negating the need for any additional sources for readers to start work in the area; Presents a unique method of investigation of discontinuous almost periodic solutions in its unified form, employed to differential equations with different types of discontinuity; Develops the equivalence method to its ultimate effective state such that most important theoretical problems and practical applications can be analyzed by the method.

Stability and Control of Large-Scale Dynamical Systems

Author : Wassim M. Haddad
Publisher : Princeton University Press
ISBN 13 : 1400842662
Total Pages : 389 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Stability and Control of Large-Scale Dynamical Systems by : Wassim M. Haddad

Download or read book Stability and Control of Large-Scale Dynamical Systems written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2011-11-14 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.

Stability Theory of Dynamical Systems

Author : N.P. Bhatia
Publisher : Springer Science & Business Media
ISBN 13 : 9783540427483
Total Pages : 252 pages
Book Rating : 4.4/5 (274 download)

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Book Synopsis Stability Theory of Dynamical Systems by : N.P. Bhatia

Download or read book Stability Theory of Dynamical Systems written by N.P. Bhatia and published by Springer Science & Business Media. This book was released on 2002-01-10 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reprint of classic reference work. Over 400 books have been published in the series Classics in Mathematics, many remain standard references for their subject. All books in this series are reissued in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. "... The book has many good points: clear organization, historical notes and references at the end of every chapter, and an excellent bibliography. The text is well-written, at a level appropriate for the intended audience, and it represents a very good introduction to the basic theory of dynamical systems."

Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales

Author : Chao Wang
Publisher : Springer Nature
ISBN 13 : 3031112369
Total Pages : 195 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales by : Chao Wang

Download or read book Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales written by Chao Wang and published by Springer Nature. This book was released on 2022-09-20 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales. Several applications are studied; in particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems) is presented. The results are not only effective on classical fuzzy dynamic systems, including their continuous and discrete situations, but are also valid for other fuzzy multidimensional dynamic systems on various hybrid domains. In an effort to achieve more accurate analysis in real world applications, the authors propose a number of uncertain factors in the theory. As such, fuzzy dynamical models, interval-valued functions, differential equations, fuzzy-valued differential equations, and their applications to dynamic equations on time scales are considered.