Global Differential Dynamics
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Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds
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Author : Taeyoung Lee
language : en
Publisher: Springer
Release Date : 2017-08-14
Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds written by Taeyoung Lee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-14 with Mathematics categories.
This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.
Differential Dynamical Systems Revised Edition
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Author : James D. Meiss
language : en
Publisher: SIAM
Release Date : 2017-01-24
Differential Dynamical Systems Revised Edition written by James D. Meiss and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Mathematics categories.
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.
A General Mathematical Theory Of The Dynamic Global Political Economy
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Author : David W K Yeung
language : en
Publisher: World Scientific
Release Date : 2024-09-24
A General Mathematical Theory Of The Dynamic Global Political Economy written by David W K Yeung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-24 with Mathematics categories.
William Jevons (1866 and 1871) established a ground-breaking milestone with 'A General Mathematical Theory of Political Economy' for economic analysis. Jevons' work was praised as the start of the mathematical method in the discipline of economics, which is inherently a subject involved with mathematics and quantities. This book focuses on the most fast-evolving and encompassing area in political economy — the dynamic global political economy. Under the high level of globalization currently, intertemporal and cross-boundary interactive elements are present in political-economic encounters. Indeed, almost all studies in the political economy may fall into the study of dynamic global political economy. Since the world has changed significantly, new mathematics developed by the authors of this book is used to formulate a general mathematical theory for the dynamic global political economy nowadays. A distinctive feature of the current book is that it combines advanced mathematics, game-theoretic concepts, and economics to develop a general mathematical theory supporting the study of the dynamic global political economy.The book covers mathematical theory for different areas of the dynamic global political economy. In addition, it explicates the application of the mathematical theory in real-world scenarios, including (i) environmental degradation under an uncoordinated interaction scenario, (ii) global climate accords with collaboration and cooperation, (iii) trade network involving the Belt-Road Initiative (BRI) and Build Back Better World (B3W) Initiative, and (iv) random termination of international joint ventures.
Global Attractors Of Non Autonomous Dissipative Dynamical Systems
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Author : David N. Cheban
language : en
Publisher: World Scientific
Release Date : 2004
Global Attractors Of Non Autonomous Dissipative Dynamical Systems written by David N. Cheban and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor.
Advances In Epidemiological Modeling And Control Of Viruses
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Author : Hemen Dutta
language : en
Publisher: Elsevier
Release Date : 2023-01-06
Advances In Epidemiological Modeling And Control Of Viruses written by Hemen Dutta and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-06 with Medical categories.
Advances in Epidemiological Modeling and Control of Viruses covers recent and advanced research works in the field of epidemiological modeling, with special emphasis on new strategies to control the occurrence and reoccurrence of viruses. The models included in this book can be used to study the dynamics of different viruses, searching for control measures, and epidemic models under various effects and environments. This book covers different models and methods of modeling, including data-driven approaches. The authors and editors are experienced researchers, and each chapter has been designed to provide readers with leading-edge information on topics discussed. - Includes models to describe global and local dynamics of various viruses - Provides readers with control strategies for occurrence and reoccurrence of viruses - Includes epidemic models under various effects and environments - Provides readers with a robust set of mathematical tools and techniques for epidemiological modeling
Delay Differential Equations
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Author : Yang Kuang
language : en
Publisher: Academic Press
Release Date : 1993-03-05
Delay Differential Equations written by Yang Kuang and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-05 with Mathematics categories.
Delay Differential Equations emphasizes the global analysis of full nonlinear equations or systems. The book treats both autonomous and nonautonomous systems with various delays. Key topics addressed are the possible delay influence on the dynamics of the system, such as stability switching as time delay increases, the long time coexistence of populations, and the oscillatory aspects of the dynamics. The book also includes coverage of the interplay of spatial diffusion and time delays in some diffusive delay population models. The treatment presented in this monograph will be of great value in the study of various classes of DDEs and their multidisciplinary applications.
Differential Equations And Dynamical Systems
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Author : Lawrence Perko
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Differential Equations And Dynamical Systems written by Lawrence Perko 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.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.
Global Attractors Of Nonautonomous Dissipative Dynamical Systems
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Author : David N Cheban
language : en
Publisher: World Scientific
Release Date : 2004-11-29
Global Attractors Of Nonautonomous Dissipative Dynamical Systems written by David N Cheban and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-29 with Mathematics categories.
The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor. From an in-depth introduction to the different types of dissipativity and attraction, the book takes a comprehensive look at the connections between them, and critically discusses applications of general results to different classes of differential equations. Intended for experts in qualitative theory of differential equations, dynamical systems and their applications, this accessible book can also serve as an important resource for senior students and lecturers.
Differential Equations Dynamical Systems And An Introduction To Chaos
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Author : Morris W. Hirsch
language : en
Publisher: Academic Press
Release Date : 2004
Differential Equations Dynamical Systems And An Introduction To Chaos written by Morris W. Hirsch and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Business & Economics categories.
Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.
Handbook Of Mathematical Fluid Dynamics
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Author : S. Friedlander
language : en
Publisher: Elsevier
Release Date : 2007-05-16
Handbook Of Mathematical Fluid Dynamics written by S. Friedlander and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-16 with Science categories.
This is the fourth volume in a series of survey articles covering many aspects of mathematical fluid dynamics, a vital source of open mathematical problems and exciting physics.