Modeling And Computations In Dynamical Systems

Author : James D. Meiss
Publisher : SIAM
Page : 392 pages
File Size : 42,6 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9781611974645

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Differential Dynamical Systems, Revised Edition by James D. Meiss Pdf

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.

Author : Patricia Melin,Oscar Castillo
Publisher : CRC Press
Page : 262 pages
File Size : 42,7 Mb
Release : 2001-10-25
Category : Mathematics
ISBN : 9781420024524

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Modelling, Simulation and Control of Non-linear Dynamical Systems by Patricia Melin,Oscar Castillo Pdf

These authors use soft computing techniques and fractal theory in this new approach to mathematical modeling, simulation and control of complexion-linear dynamical systems. First, a new fuzzy-fractal approach to automated mathematical modeling of non-linear dynamical systems is presented. It is illustrated with examples on the PROLOG programming la

Author : P. P. J. van den Bosch,A. C. van der Klauw
Publisher : CRC Press
Page : 212 pages
File Size : 55,5 Mb
Release : 2020-12-17
Category : Mathematics
ISBN : 9780429605925

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Modeling, Identification and Simulation of Dynamical Systems by P. P. J. van den Bosch,A. C. van der Klauw Pdf

This book gives an in-depth introduction to the areas of modeling, identification, simulation, and optimization. These scientific topics play an increasingly dominant part in many engineering areas such as electrotechnology, mechanical engineering, aerospace, and physics. This book represents a unique and concise treatment of the mutual interactions among these topics. Techniques for solving general nonlinear optimization problems as they arise in identification and many synthesis and design methods are detailed. The main points in deriving mathematical models via prior knowledge concerning the physics describing a system are emphasized. Several chapters discuss the identification of black-box models. Simulation is introduced as a numerical tool for calculating time responses of almost any mathematical model. The last chapter covers optimization, a generally applicable tool for formulating and solving many engineering problems.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 43,6 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9789814478984

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Modeling and Computations in Dynamical Systems by Anonim Pdf

Author : Maurizio Bottoni
Publisher : Springer Nature
Page : 541 pages
File Size : 43,8 Mb
Release : 2021-11-12
Category : Technology & Engineering
ISBN : 9783030797171

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Physical Modeling and Computational Techniques for Thermal and Fluid-dynamics by Maurizio Bottoni Pdf

This book on computational techniques for thermal and fluid-dynamic problems arose from seminars given by the author at the Institute of Nuclear Energy Technology of Tsinghua University in Beijing, China. The book is composed of eight chapters-- some of which are characterized by a scholastic approach, others are devoted to numerical solution of ordinary differential equations of first order, and of partial differential equations of first and second order, respectively. In Chapter IV, basic concepts of consistency, stability and convergence of discretization algorithms are covered in some detail. Other parts of the book follow a less conventional approach, mainly informed by the author’s experience in teaching and development of computer programs. Among these is Chapter III, where the residual method of Orthogonal Collocations is presented in several variants, ranging from the classical Galerkin method to Point and Domain Collocations, applied to numerical solution of partial differential equations of first order. In most cases solutions of fluid dynamic problems are led through the discretization process, to the numerical solutions of large linear systems. Intended to impart a basic understanding of numerical techniques that would enable readers to deal with problems of Computational Fluid Dynamics at research level, the book is ideal as a reference for graduate students, researchers, and practitioners.

Author : Lisa J. Fauci,Shay Gueron
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461301516

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Computational Modeling in Biological Fluid Dynamics by Lisa J. Fauci,Shay Gueron Pdf

This IMA Volume in Mathematics and its Applications COMPUTATIONAL MODELING IN BIOLOGICAL FLUID DYNAMICS is based on the proceedings of a very successful workshop with the same title. The workshop was an integral part of the September 1998 to June 1999 IMA program on "MATHEMATICS IN BIOLOGY." I would like to thank the organizing committee: Lisa J. Fauci of Tulane University and Shay Gueron of Technion - Israel Institute of Technology for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda tion (NSF), whose financial support of the IMA made the Mathematics in Biology program possible. Willard Miller, Jr., Professor and Director Institute for Mathematics and its Applications University of Minnesota 400 Lind Hall, 207 Church St. SE Minneapolis, MN 55455-0436 612-624-6066, FAX 612-626-7370 [email protected] World Wide Web: http://www.ima.umn.edu v PREFACE A unifying theme in biological fluid dynamics is the interaction of moving, elastic boundaries with a surrounding fluid. A complex dynami cal system describes the motion of red blood cells through the circulatory system, the movement of spermatazoa in the reproductive tract, cilia of microorganisms, or a heart pumping blood. The revolution in computa tional technology has allowed tremendous progress in the study of these previously intractable fluid-structure interaction problems.

Author : Pawel Olejnik,Jan Awrejcewicz,Michal Fečkan
Publisher : World Scientific Publishing Company
Page : 262 pages
File Size : 53,6 Mb
Release : 2017-07-07
Category : Social Science
ISBN : 9813225289

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Modeling, Analysis and Control of Dynamical Systems by Pawel Olejnik,Jan Awrejcewicz,Michal Fečkan Pdf

This book is aimed primarily towards physicists and mechanical engineers specializing in modeling, analysis, and control of discontinuous systems with friction and impacts. It fills a gap in the existing literature by offering an original contribution to the field of discontinuous mechanical systems based on mathematical and numerical modeling as well as the control of such systems. Each chapter provides the reader with both the theoretical background and results of verified and useful computations, including solutions of the problems of modeling and application of friction laws in numerical computations, results from finding and analyzing impact solutions, the analysis and control of dynamical systems with discontinuities, etc. The contents offer a smooth correspondence between science and engineering and will allow the reader to discover new ideas. Also emphasized is the unity of diverse branches of physics and mathematics towards understanding complex piecewise-smooth dynamical systems. Mathematical models presented will be important in numerical experiments, experimental measurements, and optimization problems found in applied mechanics. Sample Chapter(s)

Author : N.H. McClamroch
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461260875

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State Models of Dynamic Systems by N.H. McClamroch Pdf

The purpose of this book is to expose undergraduate students to the use of applied mathematics and physical argument as a basis for developing an understanding of the response characteristics, from a systems viewpoint, of a broad class of dynamic physical processes. This book was developed for use in the course ECE 355, Dynamic Systems and Modeling, in the Department of Electrical and Computer Engineering at the University of Michigan, Ann Arbor. The course ECE 355 has been elected primarily by junior and senior level students in computer engineering or in electrical engineering. Occasionally a student from outside these two programs elected the course. Thus the book is written with this class of students in mind. It is assumed that the reader has previous background in mathematics through calculus, differential equations, and Laplace transforms, in elementary physics, and in elemen tary mechanics and circuits. Although these prerequisites indicate the orientation of the material, the book should be accessible and of interest to students with a much wider spectrum of experience in applied mathemati cal topics. The subject matter of the book can be considered to form an introduc tion to the theory of mathematical systems presented from a modern, as opposed to a classical, point of view. A number of physical processes are examined where the underlying systems concepts can be clearly seen and grasped. The organization of the book around case study examples has evolved as a consequence of student suggestions.

Author : Wojciech Mitkowski
Publisher : Springer
Page : 192 pages
File Size : 42,9 Mb
Release : 2009-05-02
Category : Mathematics
ISBN : 9783540922032

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Modelling Dynamics in Processes and Systems by Wojciech Mitkowski Pdf

Dynamics is what characterizes virtually all phenomenae we face in the real world, and processes that proceed in practically all kinds of inanimate and animate systems, notably social systems. For our purposes dynamics is viewed as time evolution of some characteristic features of the phenomenae or processes under consideration. It is obvious that in virtually all non-trivial problems dynamics can not be neglected, and should be taken into account in the analyses to, first, get insight into the problem consider, and second, to be able to obtain meaningful results. A convenient tool to deal with dynamics and its related evolution over time is to use the concept of a dynamic system which, for the purposes of this volume can be characterized by the input (control), state and output spaces, and a state transition equation. Then, starting from an initial state, we can find a sequence of consecutive states (outputs) under consecutive inputs (controls). That is, we obtain a trajectory. The state transition equation may be given in various forms, exemplified by differential and difference equations, linear or nonlinear, deterministic or stochastic, or even fuzzy (imprecisely specified), fully or partially known, etc. These features can give rise to various problems the analysts may encounter like numerical difficulties, instability, strange forms of behavior (e.g. chaotic), etc. This volume is concerned with some modern tools and techniques which can be useful for the modeling of dynamics. We focus our attention on two important areas which play a key role nowadays, namely automation and robotics, and biological systems. We also add some new applications which can greatly benefit from the availability of effective and efficient tools for modeling dynamics, exemplified by some applications in security systems.

Author : Erik M. Bollt,Naratip Santitissadeekorn
Publisher : SIAM
Page : 376 pages
File Size : 50,5 Mb
Release : 2013-12-03
Category : Mathematics
ISBN : 9781611972641

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Applied and Computational Measurable Dynamics by Erik M. Bollt,Naratip Santitissadeekorn Pdf

Until recently, measurable dynamics has been held as a highly theoretcal mathematical topic with few generally known obvious links for practitioners in areas of applied mathematics. However, the advent of high-speed computers, rapidly developing algorithms, and new numerical methods has allowed for a tremendous amount of progress and sophistication in efforts to represent the notion of a transfer operator discretely but to high resolution. This book connects many concepts in dynamical systems with mathematical tools from areas such as graph theory and ergodic theory. The authors introduce practical tools for applications related to measurable dynamical systems, coherent structures, and transport problems. The new and fast-developing computational tools discussed throughout the book allow for detailed analysis of real-world problems that are simply beyond the reach of traditional methods.

Author : Elbert E. N. Macau
Publisher : Springer
Page : 228 pages
File Size : 40,8 Mb
Release : 2018-06-14
Category : Technology & Engineering
ISBN : 9783319785127

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A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems by Elbert E. N. Macau Pdf

This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry groups, conservation laws, risk reduction management, barriers in Hamiltonian systems, and synchronization and chaotic transient. Illustrating mathematical modeling applications to nonlinear physics and nonlinear engineering, the book is ideal for academic and industrial researchers concerned with machinery and controls, manufacturing, and controls. · Introduces new concepts for understanding and modeling complex systems; · Explains risk reduction management in complex systems; · Examines the symmetry group approach to understanding complex systems; · Illustrates the relation between transient chaos and crises.

Author : Eugene M. Izhikevich
Publisher : MIT Press
Page : 459 pages
File Size : 48,7 Mb
Release : 2010-01-22
Category : Medical
ISBN : 9780262514200

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Dynamical Systems in Neuroscience by Eugene M. Izhikevich Pdf

Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum—or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.

Author : Dhruv Khandelwal
Publisher : Springer Nature
Page : 250 pages
File Size : 55,7 Mb
Release : 2022-02-03
Category : Technology & Engineering
ISBN : 9783030903435

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Automating Data-Driven Modelling of Dynamical Systems by Dhruv Khandelwal Pdf

This book describes a user-friendly, evolutionary algorithms-based framework for estimating data-driven models for a wide class of dynamical systems, including linear and nonlinear ones. The methodology addresses the problem of automating the process of estimating data-driven models from a user’s perspective. By combining elementary building blocks, it learns the dynamic relations governing the system from data, giving model estimates with various trade-offs, e.g. between complexity and accuracy. The evaluation of the method on a set of academic, benchmark and real-word problems is reported in detail. Overall, the book offers a state-of-the-art review on the problem of nonlinear model estimation and automated model selection for dynamical systems, reporting on a significant scientific advance that will pave the way to increasing automation in system identification.

Author : Ricardo Zavala Yoe
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 50,5 Mb
Release : 2008-05-30
Category : Computers
ISBN : 9783540787341

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Modelling and Control of Dynamical Systems: Numerical Implementation in a Behavioral Framework by Ricardo Zavala Yoe Pdf

The Behavioral Approach for systems and control deals directly with the solution of the differential equations which represent the system. This book reviews this approach and offers new theoretic results. The programs and algorithms are MATLAB based.

Author : A. J. Roberts
Publisher : SIAM
Page : 760 pages
File Size : 42,6 Mb
Release : 2014-12-18
Category : Mathematics
ISBN : 9781611973556

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Model Emergent Dynamics in Complex Systems by A. J. Roberts Pdf

Arising out of the growing interest in and applications of modern dynamical systems theory, this book explores how to derive relatively simple dynamical equations that model complex physical interactions. The author’s objectives are to use sound theory to explore algebraic techniques, develop interesting applications, and discover general modeling principles. Model Emergent Dynamics in Complex Systems unifies into one powerful and coherent approach the many varied extant methods for mathematical model reduction and approximation. Using mathematical models at various levels of resolution and complexity, the book establishes the relationships between such multiscale models and clarifying difficulties and apparent paradoxes and addresses model reduction for systems, resolves initial conditions, and illuminates control and uncertainty. The basis for the author’s methodology is the theory and the geometric picture of both coordinate transforms and invariant manifolds in dynamical systems; in particular, center and slow manifolds are heavily used. The wonderful aspect of this approach is the range of geometric interpretations of the modeling process that it produces—simple geometric pictures inspire sound methods of analysis and construction. Further, pictures drawn of state spaces also provide a route to better assess a model’s limitations and strengths. Geometry and algebra form a powerful partnership and coordinate transforms and manifolds provide a powerfully enhanced and unified view of a swathe of other complex system modeling methodologies such as averaging, homogenization, multiple scales, singular perturbations, two timing, and WKB theory. Audience Advanced undergraduate and graduate students, engineers, scientists, and other researchers who need to understand systems and modeling at different levels of resolution and complexity will all find this book useful.