Dynamic Systems On Measure Chains

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Dynamic Systems on Measure Chains

Author : V. Lakshmikantham
Publisher : Springer Science & Business Media
ISBN 13 : 1475724497
Total Pages : 300 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Dynamic Systems on Measure Chains by : V. Lakshmikantham

Download or read book Dynamic Systems on Measure Chains written by V. Lakshmikantham and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a modelling point of view, it is more realistic to model a phenomenon by a dynamic system which incorporates both continuous and discrete times, namely, time as an arbitrary closed set of reals called time-scale or measure chain. It is therefore natural to ask whether it is possible to provide a framework which permits us to handle both dynamic systems simultaneously so that one can get some insight and a better understanding of the subtle differences of these two different systems. The answer is affirmative, and recently developed theory of dynamic systems on time scales offers the desired unified approach. In this monograph, we present the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on time scales. In chapter two, we introduce dynamic systems on time scales and prove the basic properties of solutions of such dynamic systems. The theory of Lyapunov stability is discussed in chapter three in an appropriate setup. Chapter four is devoted to describing several different areas of investigations of dynamic systems on time scales which will provide an exciting prospect and impetus for further advances in this important area which is very new. Some important features of the monograph are as follows: It is the first book that is dedicated to a systematic development of the theory of dynamic systems on time scales which is of recent origin. It demonstrates the interplay of the two different theories, namely, the theory of continuous and discrete dynamic systems, when imbedded in one unified framework. It provides an impetus to investigate in the setup of time scales other important problems which might offer a better understanding of the intricacies of a unified study.£/LIST£ Audience: The readership of this book consists of applied mathematicians, engineering scientists, research workers in dynamic systems, chaotic theory and neural nets.

Method of Variation of Parameters for Dynamic Systems

Author : V. Lakshmikantham
Publisher : Routledge
ISBN 13 : 1351431951
Total Pages : 330 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Method of Variation of Parameters for Dynamic Systems by : V. Lakshmikantham

Download or read book Method of Variation of Parameters for Dynamic Systems written by V. Lakshmikantham and published by Routledge. This book was released on 2019-09-10 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Method of Variation of Parameters for Dynamic Systems presents a systematic and unified theory of the development of the theory of the method of variation of parameters, its unification with Lyapunov's method and typical applications of these methods. No other attempt has been made to bring all the available literature into one volume. This book is a clear exposition of this important topic in control theory, which is not covered by any other text. Such an exposition finally enables the comparison and contrast of the theory and the applications, thus facilitating further development in this fascinating field.

Dynamic Equations on Time Scales

Author : Martin Bohner
Publisher : Springer Science & Business Media
ISBN 13 : 1461202019
Total Pages : 365 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Dynamic Equations on Time Scales by : Martin Bohner

Download or read book Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.

Advances in Dynamic Equations on Time Scales

Author : Martin Bohner
Publisher : Springer Science & Business Media
ISBN 13 : 0817682309
Total Pages : 354 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Advances in Dynamic Equations on Time Scales by : Martin Bohner

Download or read book Advances in Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory material on the calculus of time scales and dynamic equations.; Numerous examples and exercises illustrate the diverse application of dynamic equations on time scales.; Unified and systematic exposition of the topics allows good transitions from chapter to chapter.; Contributors include Anderson, M. Bohner, Davis, Dosly, Eloe, Erbe, Guseinov, Henderson, Hilger, Hilscher, Kaymakcalan, Lakshmikantham, Mathsen, and A. Peterson, founders and leaders of this field of study.; Useful as a comprehensive resource of time scales and dynamic equations for pure and applied mathematicians.; Comprehensive bibliography and index complete this text.

Theory of Translation Closedness for Time Scales

Author : Chao Wang
Publisher : Springer Nature
ISBN 13 : 3030386449
Total Pages : 586 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Theory of Translation Closedness for Time Scales by : Chao Wang

Download or read book Theory of Translation Closedness for Time Scales written by Chao Wang and published by Springer Nature. This book was released on 2020-05-05 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.

Dynamic Inequalities On Time Scales

Author : Ravi Agarwal
Publisher : Springer
ISBN 13 : 3319110020
Total Pages : 264 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Dynamic Inequalities On Time Scales by : Ravi Agarwal

Download or read book Dynamic Inequalities On Time Scales written by Ravi Agarwal and published by Springer. This book was released on 2014-10-30 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics. In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Čebyšv's inequality. Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail.

Communications in Difference Equations

Author : Saber N. Elaydi
Publisher : CRC Press
ISBN 13 : 9789056996888
Total Pages : 452 pages
Book Rating : 4.9/5 (968 download)

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Book Synopsis Communications in Difference Equations by : Saber N. Elaydi

Download or read book Communications in Difference Equations written by Saber N. Elaydi and published by CRC Press. This book was released on 2000-07-06 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of carefully refereed and edited papers were originally presented at the Fourth International Conference on Difference Equations held in Poznan, Poland. Contributions were from a diverse group of researchers from several countries and featured discussions on the theory of difference equations, open problems and conjectures, as well as related applications. Whether new to the area of research, or a veteran, this volume will be a valuable resource on the recent advances in the field of difference equations.

Proceedings of the Sixth International Conference on Difference Equations Augsburg, Germany 2001

Author : Bernd Aulbach
Publisher : CRC Press
ISBN 13 : 9780203575437
Total Pages : 590 pages
Book Rating : 4.5/5 (754 download)

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Book Synopsis Proceedings of the Sixth International Conference on Difference Equations Augsburg, Germany 2001 by : Bernd Aulbach

Download or read book Proceedings of the Sixth International Conference on Difference Equations Augsburg, Germany 2001 written by Bernd Aulbach and published by CRC Press. This book was released on 2004-06-07 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises selected papers presented at the Sixth International Conference on Difference Equations which was held at Augsburg, Germany. It covers all themes in the fields of discrete dynamical systems and ordinary and partial difference equations, classical and contemporary, theoretical and applied. It provides a useful reference text for graduates and researchers working in this area of mathematics.

Combined Measure and Shift Invariance Theory of Time Scales and Applications

Author : Chao Wang
Publisher : Springer Nature
ISBN 13 : 3031116194
Total Pages : 443 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Combined Measure and Shift Invariance Theory of Time Scales and Applications by : Chao Wang

Download or read book Combined Measure and Shift Invariance Theory of Time Scales and Applications written by Chao Wang and published by Springer Nature. This book was released on 2022-09-22 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales. First proposed by S. Hilger, the time scale theory—a unified view of continuous and discrete analysis—has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains. As a new and exciting type of mathematics—and more comprehensive and versatile than the traditional theories of differential and difference equations—, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences. Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.

Dynamics of Continuous, Discrete and Impulsive Systems

Author :
Publisher :
ISBN 13 :
Total Pages : 668 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Dynamics of Continuous, Discrete and Impulsive Systems by :

Download or read book Dynamics of Continuous, Discrete and Impulsive Systems written by and published by . This book was released on 1999 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Functional Dynamic Equations on Time Scales

Author : Svetlin G. Georgiev
Publisher : Springer
ISBN 13 : 3030154203
Total Pages : 886 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 886 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 : 3111185192
Total Pages : 370 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 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonoscillation and Oscillation Theory for Functional Differential Equations

Author : Ravi P. Agarwal
Publisher : CRC Press
ISBN 13 : 0203025741
Total Pages : 392 pages
Book Rating : 4.2/5 (3 download)

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Book Synopsis Nonoscillation and Oscillation Theory for Functional Differential Equations by : Ravi P. Agarwal

Download or read book Nonoscillation and Oscillation Theory for Functional Differential Equations written by Ravi P. Agarwal and published by CRC Press. This book was released on 2004-08-30 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes the qualitative theory of differential equations with or without delays, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology. The authors address oscillatory and nonoscillatory properties of first-order delay and neutral delay differential eq

Stability Theory for Dynamic Equations on Time Scales

Author : Anatoly A. Martynyuk
Publisher : Birkhäuser
ISBN 13 : 3319422138
Total Pages : 233 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Stability Theory for Dynamic Equations on Time Scales by : Anatoly A. Martynyuk

Download or read book Stability Theory for Dynamic Equations on Time Scales written by Anatoly A. Martynyuk and published by Birkhäuser. This book was released on 2016-09-22 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”Mathematical analysis on time scales accomplishes exactly this. This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.

Journal of Dynamic Systems, Measurement, and Control

Author :
Publisher :
ISBN 13 :
Total Pages : 772 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Journal of Dynamic Systems, Measurement, and Control by :

Download or read book Journal of Dynamic Systems, Measurement, and Control written by and published by . This book was released on 2001 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publishes theoretical and applied original papers in dynamic systems. Theoretical papers present new theoretical developments and knowledge for controls of dynamical systems together with clear engineering motivation for the new theory. Applied papers include modeling, simulation, and corroboration of theory with emphasis on demonstrated practicality.

Modeling, Dynamics, Optimization and Bioeconomics II

Author : Alberto A. Pinto
Publisher : Springer
ISBN 13 : 3319552368
Total Pages : 531 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Modeling, Dynamics, Optimization and Bioeconomics II by : Alberto A. Pinto

Download or read book Modeling, Dynamics, Optimization and Bioeconomics II written by Alberto A. Pinto and published by Springer. This book was released on 2017-09-30 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concepts and techniques presented in this volume originated from the fields of dynamics, statistics, control theory, computer science and informatics, and are applied to novel and innovative real-world applications. Over the past few decades, the use of dynamic systems, control theory, computing, data mining, machine learning and simulation has gained the attention of numerous researchers from all over the world. Admirable scientific projects using both model-free and model-based methods coevolved at today’s research centers and are introduced in conferences around the world, yielding new scientific advances and helping to solve important real-world problems. One important area of progress is the bioeconomy, where advances in the life sciences are used to produce new products in a sustainable and clean manner. In this book, scientists from all over the world share their latest insights and important findings in the field. The majority of the contributed papers for this volume were written by participants of the 3rd International Conference on Dynamics, Games and Science, DGSIII, held at the University of Porto in February 2014, and at the Berkeley Bioeconomy Conference at the University of California at Berkeley in March 2014. The aim of the project of this book “Modeling, Dynamics, Optimization and Bioeconomics II” follows the same aim as its companion piece, “Modeling, Dynamics, Optimization and Bioeconomics I,” namely, the exploration of emerging and cutting-edge theories and methods for modeling, optimization, dynamics and bioeconomy.

Attractivity and Bifurcation for Nonautonomous Dynamical Systems

Author : Martin Rasmussen
Publisher : Springer Science & Business Media
ISBN 13 : 3540712240
Total Pages : 222 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Attractivity and Bifurcation for Nonautonomous Dynamical Systems by : Martin Rasmussen

Download or read book Attractivity and Bifurcation for Nonautonomous Dynamical Systems written by Martin Rasmussen and published by Springer Science & Business Media. This book was released on 2007-06-08 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions.