Stability Theory For Dynamic Equations On Time Scales
DOWNLOAD
Download Stability Theory For Dynamic Equations On Time Scales PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Stability Theory For Dynamic Equations On Time Scales book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Stability Theory For Dynamic Equations On Time Scales
DOWNLOAD
Author : Anatoly A. Martynyuk
language : en
Publisher: Birkhäuser
Release Date : 2016-09-22
Stability Theory For Dynamic Equations On Time Scales written by Anatoly A. Martynyuk and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-22 with Mathematics categories.
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.
Stability Theory For Dynamic Equations On Time Scales
DOWNLOAD
Author : Jack Noah
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-06-07
Stability Theory For Dynamic Equations On Time Scales written by Jack Noah and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-07 with categories.
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.
Dynamic Inequalities On Time Scales
DOWNLOAD
Author : Ravi Agarwal
language : en
Publisher: Springer
Release Date : 2014-10-30
Dynamic Inequalities On Time Scales written by Ravi Agarwal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-30 with Mathematics categories.
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.
Dynamic Equations On Time Scales
DOWNLOAD
Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-15
Dynamic Equations On Time Scales written by Martin Bohner 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 2001-06-15 with Language Arts & Disciplines categories.
The study of dynamic equations on a measure chain (time scale) goes back to its founder S. Hilger (1988), and is a new area of still fairly theoretical exploration in mathematics. Motivating the subject is the notion that dynamic equations on measure chains can build bridges between continuous and discrete mathematics. Further, the study of measure chain theory has led to several important applications, e.g., in the study of insect population models, neural networks, heat transfer, and epidemic models. Key features of the book: * Introduction to measure chain theory; discussion of its usefulness in allowing for the simultaneous development of differential equations and difference equations without having to repeat analogous proofs * Many classical formulas or procedures for differential and difference equations cast in a new light * New analogues of many of the "special functions" studied * Examination of the properties of the "exponential function" on time scales, which can be defined and investigated using a particularly simple linear equation * Additional topics covered: self-adjoint equations, linear systems, higher order equations, dynamic inequalities, and symplectic dynamic systems * Clear, motivated exposition, beginning with preliminaries and progressing to more sophisticated text * Ample examples and exercises throughout the book * Solutions to selected problems Requiring only a first semester of calculus and linear algebra, Dynamic Equations on Time Scales may be considered as an interesting approach to differential equations via exposure to continuous and discrete analysis. This approach provides an early encounter with many applications in such areas as biology, physics, and engineering. Parts of the book may be used in a special topics seminar at the senior undergraduate or beginning graduate levels. Finally, the work may
Advances In Dynamic Equations On Time Scales
DOWNLOAD
Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-12-06
Advances In Dynamic Equations On Time Scales written by Martin Bohner 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 2002-12-06 with Mathematics categories.
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.
Dynamic Systems On Measure Chains
DOWNLOAD
Author : V. Lakshmikantham
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Dynamic Systems On Measure Chains written by V. Lakshmikantham 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 2013-06-29 with Mathematics categories.
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: Thereadership of this book consists of applied mathematicians, engineering scientists, research workers in dynamic systems, chaotic theory and neural nets.
Advances In Dynamic Equations On Time Scales
DOWNLOAD
Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Advances In Dynamic Equations On Time Scales written by Martin Bohner 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 2011-06-28 with Mathematics categories.
The development of time scales is still in its infancy, yet as inroads are made, interest is gathering steam. Of a great deal of interest are methods being intro duced for dynamic equations on time scales, which now explain some discrepancies that have been encountered when results for differential equations and their dis crete counterparts have been independently considered. The explanations of these seeming discrepancies are incidentally producing unifying results via time scales methods. The study of dynamic equations on time scales is a fairly new subject, and research in this area is rapidly growing. It has been created in order to unify continuous and discrete analysis, and it allows a simultaneous treatment of dif ferential and difference equations, extending those theories to so-called dynamic equations. An introduction to this subject is given in Dynamic Equations on Time Scales: An Introduction with Applications (MARTIN BOHNER and ALLAN PETER SON, Birkhauser, 2001 [86]). The current book is designed to supplement this introduction and to offer access to the vast literature that has already emerged in this field. It consists of ten chapters, written by an international team of 21 experts in their areas, thus providing an overview of the recent advances in the theory on time scales. We want to emphasize here that this book is not just a collection of papers by different authors.
Dynamic Equations On Time Scales
DOWNLOAD
Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Dynamic Equations On Time Scales written by Martin Bohner 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.
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.
Theory Of Translation Closedness For Time Scales
DOWNLOAD
Author : Chao Wang
language : en
Publisher: Springer Nature
Release Date : 2020-05-05
Theory Of Translation Closedness For Time Scales written by Chao Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-05 with Mathematics categories.
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.
Power System Dynamics And Stability
DOWNLOAD
Author : Peter W. Sauer
language : en
Publisher:
Release Date : 1998
Power System Dynamics And Stability written by Peter W. Sauer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Technology & Engineering categories.
For a one-semester senior or beginning graduate level course in power system dynamics. This text begins with the fundamental laws for basic devices and systems in a mathematical modeling context. It includes systematic derivations of standard synchronous machine models with their fundamental controls. These individual models are interconnected for system analysis and simulation. Singular perturbation is used to derive and explain reduced-order models.