Dynamic Systems On Measure Chains

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Dynamic Systems On Measure Chains

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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: The readership of this book consists of applied mathematicians, engineering scientists, research workers in dynamic systems, chaotic theory and neural nets.

Dynamic Equations On Time Scales

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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.

Method Of Variation Of Parameters For Dynamic Systems

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Author : V. Lakshmikantham
language : en
Publisher: Routledge
Release Date : 2019-09-10

Method Of Variation Of Parameters For Dynamic Systems written by V. Lakshmikantham and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-10 with Mathematics categories.

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.

Advances In Dynamic Equations On Time Scales

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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.

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.

Extremes And Recurrence In Dynamical Systems

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Author : Valerio Lucarini
language : en
Publisher: John Wiley & Sons
Release Date : 2016-04-25

Extremes And Recurrence In Dynamical Systems written by Valerio Lucarini 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 2016-04-25 with Mathematics categories.

Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.

Dynamical Systems In Theoretical Perspective

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Author : Jan Awrejcewicz
language : en
Publisher: Springer
Release Date : 2018-09-01

Dynamical Systems In Theoretical Perspective written by Jan Awrejcewicz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-01 with Mathematics categories.

This book focuses on theoretical aspects of dynamical systems in the broadest sense. It highlights novel and relevant results on mathematical and numerical problems that can be found in the fields of applied mathematics, physics, mechanics, engineering and the life sciences. The book consists of contributed research chapters addressing a diverse range of problems. The issues discussed include (among others): numerical-analytical algorithms for nonlinear optimal control problems on a large time interval; gravity waves in a reservoir with an uneven bottom; value distribution and growth of solutions for certain Painlevé equations; optimal control of hybrid systems with sliding modes; a mathematical model of the two types of atrioventricular nodal reentrant tachycardia; non-conservative instability of cantilevered nanotubes using the Cell Discretization Method; dynamic analysis of a compliant tensegrity structure for use in a gripper application; and Jeffcott rotor bifurcation behavior using various models of hydrodynamic bearings.

Proceedings Of The Sixth International Conference On Difference Equations Augsburg Germany 2001

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Author : Bernd Aulbach
language : en
Publisher: CRC Press
Release Date : 2004-06-07

Proceedings Of The Sixth International Conference On Difference Equations Augsburg Germany 2001 written by Bernd Aulbach and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-07 with Mathematics categories.

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.

Dynamics Of Continuous Discrete And Impulsive Systems

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Author :
language : en
Publisher:
Release Date : 1999

Dynamics Of Continuous Discrete And Impulsive Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Control theory categories.

Dynamic Calculus And Equations On Time Scales

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Author : Svetlin G. Georgiev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-09-18

Dynamic Calculus And Equations On Time Scales written by Svetlin G. Georgiev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-18 with Mathematics categories.

Monotonicity In Markov Reward And Decision Chains

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Author : Ger Koole
language : en
Publisher: Now Publishers Inc
Release Date : 2007

Monotonicity In Markov Reward And Decision Chains written by Ger Koole and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Dynamic programming categories.

Monotonicity in Markov Reward and Decision Chains: Theory and Applications focuses on monotonicity results for dynamic systems that take values in the natural numbers or in more-dimensional lattices. The results are mostly formulated in terms of controlled queueing systems, but there are also applications to maintenance systems, revenue management, and so forth. The focus is on results that are obtained by inductively proving properties of the dynamic programming value function. A framework is provided for using this method that unifies results obtained for different models. The author also provides a comprehensive overview of the results that can be obtained through it, in which he discusses not only (partial) characterizations of optimal policies but also applications of monotonicity to optimization problems and the comparison of systems. Monotonicity in Markov Reward and Decision Chains: Theory and Applications is an invaluable resource for anyone planning or conducting research in this particular area. The essentials of the topic are presented in an accessible manner and an extensive bibliography guides towards further reading.