Dynamic Systems On Measure Chains

Author : V. Lakshmikantham,S. Sivasundaram,B. Kaymakcalan
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 54,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475724493

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Dynamic Systems on Measure Chains by V. Lakshmikantham,S. Sivasundaram,B. Kaymakcalan Pdf

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.

Author : V. Lakshmikantham
Publisher : Routledge
Page : 330 pages
File Size : 40,5 Mb
Release : 2019-09-10
Category : Mathematics
ISBN : 9781351431958

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Method of Variation of Parameters for Dynamic Systems by V. Lakshmikantham Pdf

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.

Author : Martin Bohner,Allan Peterson
Publisher : Springer Science & Business Media
Page : 365 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461202011

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Dynamic Equations on Time Scales by Martin Bohner,Allan Peterson Pdf

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.

Author : Martin Bohner,Allan C. Peterson
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 41,7 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9780817682309

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Advances in Dynamic Equations on Time Scales by Martin Bohner,Allan C. Peterson Pdf

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.

Author : Ravi Agarwal,Donal O'Regan,Samir Saker
Publisher : Springer
Page : 264 pages
File Size : 45,5 Mb
Release : 2014-10-30
Category : Mathematics
ISBN : 9783319110028

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Dynamic Inequalities On Time Scales by Ravi Agarwal,Donal O'Regan,Samir Saker Pdf

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.

Author : Bernd Aulbach,Saber N. Elaydi,G. Ladas
Publisher : CRC Press
Page : 590 pages
File Size : 42,5 Mb
Release : 2004-06-07
Category : Mathematics
ISBN : 0203575431

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Proceedings of the Sixth International Conference on Difference Equations Augsburg, Germany 2001 by Bernd Aulbach,Saber N. Elaydi,G. Ladas Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 668 pages
File Size : 54,9 Mb
Release : 1999
Category : Control theory
ISBN : UOM:39015049401196

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Dynamics of Continuous, Discrete and Impulsive Systems by Anonim Pdf

Author : Svetlin G. Georgiev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 370 pages
File Size : 52,5 Mb
Release : 2023-09-18
Category : Mathematics
ISBN : 9783111185194

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Dynamic Calculus and Equations on Time Scales by Svetlin G. Georgiev Pdf

Author : Chao Wang,Ravi P. Agarwal,Donal O' Regan,Rathinasamy Sakthivel
Publisher : Springer Nature
Page : 586 pages
File Size : 43,5 Mb
Release : 2020-05-05
Category : Mathematics
ISBN : 9783030386443

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Theory of Translation Closedness for Time Scales by Chao Wang,Ravi P. Agarwal,Donal O' Regan,Rathinasamy Sakthivel Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 772 pages
File Size : 54,5 Mb
Release : 2001
Category : Automatic control
ISBN : UOM:39015048306677

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Journal of Dynamic Systems, Measurement, and Control by Anonim Pdf

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.

Author : Alberto A. Pinto,David Zilberman
Publisher : Springer
Page : 532 pages
File Size : 42,8 Mb
Release : 2017-09-30
Category : Mathematics
ISBN : 9783319552361

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Modeling, Dynamics, Optimization and Bioeconomics II by Alberto A. Pinto,David Zilberman Pdf

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.

Author : Martin Rasmussen
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 45,5 Mb
Release : 2007-06-08
Category : Mathematics
ISBN : 9783540712244

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Attractivity and Bifurcation for Nonautonomous Dynamical Systems by Martin Rasmussen Pdf

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.

Author : Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily
Publisher : Springer Nature
Page : 226 pages
File Size : 42,6 Mb
Release : 2020-01-01
Category : Mathematics
ISBN : 9783030358549

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Dynamics with Chaos and Fractals by Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily Pdf

The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.

Author : Saber N. Elaydi,Jerry Popenda,Jerry Rakowski
Publisher : CRC Press
Page : 452 pages
File Size : 43,8 Mb
Release : 2000-07-06
Category : Mathematics
ISBN : 9056996886

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Communications in Difference Equations by Saber N. Elaydi,Jerry Popenda,Jerry Rakowski Pdf

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.

Author : Marat Akhmet
Publisher : Springer
Page : 360 pages
File Size : 52,9 Mb
Release : 2019-06-20
Category : Technology & Engineering
ISBN : 9783030205720

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Almost Periodicity, Chaos, and Asymptotic Equivalence by Marat Akhmet Pdf

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.