**Author**: James D. Meiss

**Publisher:**SIAM

**ISBN:**0898716357

**Category:**Mathematics

**Page:**412

**View:**7095

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# Search Results for: differential-dynamical-systems-1-monographs-on-mathematical-modeling-and-computation

**Author**: James D. Meiss

**Publisher:** SIAM

**ISBN:** 0898716357

**Category:** Mathematics

**Page:** 412

**View:** 7095

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 conceptsflow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. 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. Audience This textbook is intended for senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with elementary differential equations and linear algebra and should have had exposure to advanced calculus. Contents List of Figures; Preface; Acknowledgments; Chapter 1: Introduction; Chapter 2: Linear Systems; Chapter 3: Existence and Uniqueness; Chapter 4: Dynamical Systems; Chapter 5: Invariant Manifolds; Chapter 6: The Phase Plane; Chapter 7: Chaotic Dynamics; Chapter 8: Bifurcation Theory; Chapter 9: Hamiltonian Dynamics; Appendix: Mathematical Software; Bibliography; Index

**Author**: A. J. Roberts

**Publisher:** SIAM

**ISBN:** 9780898718225

**Category:** Calculus

**Page:** 128

**View:** 9441

Financial mathematics and its calculus introduced in an accessible manner for undergraduate students. Topics covered include financial indices as stochastic processes, Ito's stochastic calculus, the Fokker-Planck Equation and extra MATLAB/SCILAB code.
*An Introduction Via Difference and Differential Equations*

**Author**: Jacek Banasiak

**Publisher:** Cambridge University Press

**ISBN:** 1107654688

**Category:** Mathematics

**Page:** 118

**View:** 8854

Uses a wide variety of applications to demonstrate the universality of mathematical techniques in describing and analysing natural phenomena.

**Author**: Robert Smith

**Publisher:** Amer Inst of Mathematical Sciences

**ISBN:** 9781601330048

**Category:** Mathematics

**Page:** 189

**View:** 9227

*Mathematical Models in Biology, Chemistry and Population Genetics*

**Author**: Marius Ghergu,Vicentiu Radulescu

**Publisher:** Springer Science & Business Media

**ISBN:** 3642226647

**Category:** Mathematics

**Page:** 394

**View:** 8841

The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations.
*An Introduction to the Theory of Competitive and Cooperative Systems*

**Author**: Hal L. Smith

**Publisher:** American Mathematical Soc.

**ISBN:** 0821844873

**Category:** Mathematics

**Page:** 174

**View:** 2943

This book presents comprehensive treatment of a rapidly developing area with many potential applications: the theory of monotone dynamical systems and the theory of competitive and cooperative differential equations. The primary aim is to provide potential users of the theory with techniques, results, and ideas useful in applications, while at the same time providing rigorous proofs. Among the topics discussed in the book are continuous-time monotone dynamical systems, and quasimonotone and nonquasimonotone delay differential equations. The book closes with a discussion of applications to quasimonotone systems of reaction-diffusion type. Throughout the book, applications of the theory to many mathematical models arising in biology are discussed. Requiring a background in dynamical systems at the level of a first graduate course, this book is useful to graduate students and researchers working in the theory of dynamical systems and its applications.
*An Integrated Approach Across Scales*

**Author**: Daniela Calvetti,Erkki Somersalo

**Publisher:** SIAM

**ISBN:** 1611972477

**Category:** Mathematics

**Page:** 234

**View:** 2706

Interesting real-world mathematical modelling problems are complex and can usually be studied at different scales. The scale at which the investigation is carried out is one of the factors that determines the type of mathematics most appropriate to describe the problem. The book concentrates on two modelling paradigms: the macroscopic, in which phenomena are described in terms of time evolution via ordinary differential equations; and the microscopic, which requires knowledge of random events and probability. The exposition is based on this unorthodox combination of deterministic and probabilistic methodologies, and emphasizes the development of computational skills to construct predictive models. To elucidate the concepts, a wealth of examples, self-study problems, and portions of MATLAB code used by the authors are included. This book, which has been extensively tested by the authors for classroom use, is intended for students in mathematics and the physical sciences at the advanced undergraduate level and above.
*In Commemoration of the 100th Anniversary of the Birth of John von Neumann*

**Author**: N.A

**Publisher:** N.A

**ISBN:** 9814478989

**Category:**

**Page:** N.A

**View:** 2639

**Author**: Sergey Lemeshevsky, Piotr Matus, Dmitriy Poliakov

**Publisher:** Walter de Gruyter GmbH & Co KG

**ISBN:** 3110489724

**Category:**

**Page:** N.A

**View:** 2186

**Author**: G. Bard Ermentrout,David H. Terman

**Publisher:** Springer Science & Business Media

**ISBN:** 0387877088

**Category:** Mathematics

**Page:** 422

**View:** 5779

This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.
*Applications in Mechanics and Electronics*

**Author**: Vincent Acary,Bernard Brogliato

**Publisher:** Springer Science & Business Media

**ISBN:** 9783540753926

**Category:** Technology & Engineering

**Page:** 525

**View:** 3813

This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, rst because of the many app- cations in which nonsmooth models are useful, secondly because they give rise to new problems in various elds of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses. The book is divided into four parts, the rst three parts being sketched in Fig. 0. 1. The aim of the rst part is to present the main tools from mechanics and applied mathematics which are necessary to understand how nonsmooth dynamical systems may be numerically simulated in a reliable way. Many examples illustrate the th- retical results, and an emphasis is put on mechanical systems, as well as on electrical circuits (the so-called Filippov’s systems are also examined in some detail, due to their importance in control applications). The second and third parts are dedicated to a detailed presentation of the numerical schemes. A fourth part is devoted to the presentation of the software platform Siconos. This book is not a textbook on - merical analysis of nonsmooth systems, in the sense that despite the main results of numerical analysis (convergence, order of consistency, etc. ) being presented, their proofs are not provided.

**Author**: Philip Holmes

**Publisher:** Cambridge University Press

**ISBN:** 1107008255

**Category:** Science

**Page:** 386

**View:** 3706

Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.
*Theory and Applications*

**Author**: Laécio Carvalho de Barros,Rodney Carlos Bassanezi,Weldon Alexander Lodwick

**Publisher:** Springer

**ISBN:** 3662533243

**Category:** Computers

**Page:** 299

**View:** 7080

This book provides an essential introduction to the field of dynamical models. Starting from classical theories such as set theory and probability, it allows readers to draw near to the fuzzy case. On one hand, the book equips readers with a fundamental understanding of the theoretical underpinnings of fuzzy sets and fuzzy dynamical systems. On the other, it demonstrates how these theories are used to solve modeling problems in biomathematics, and presents existing derivatives and integrals applied to the context of fuzzy functions. Each of the major topics is accompanied by examples, worked-out exercises, and exercises to be completed. Moreover, many applications to real problems are presented. The book has been developed on the basis of the authors’ lectures to university students and is accordingly primarily intended as a textbook for both upper-level undergraduates and graduates in applied mathematics, statistics, and engineering. It also offers a valuable resource for practitioners such as mathematical consultants and modelers, and for researchers alike, as it may provide both groups with new ideas and inspirations for projects in the fields of fuzzy logic and biomathematics.

**Author**: Abraham Berman,Robert J. Plemmons

**Publisher:** Academic Press

**ISBN:** 1483260860

**Category:** Mathematics

**Page:** 334

**View:** 7886

Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.
*An Introduction to Theory and Applications*

**Author**: Hermann Brunner

**Publisher:** Cambridge University Press

**ISBN:** 1107098726

**Category:** Mathematics

**Page:** 410

**View:** 5083

This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations. It includes applications and an extensive bibliography.

**Author**: Lawrence Perko

**Publisher:** Springer Science & Business Media

**ISBN:** 1461300037

**Category:** Mathematics

**Page:** 557

**View:** 954

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations.
*A Dynamical Systems Viewpoint*

**Author**: Vivek S. Borkar

**Publisher:** Cambridge University Press

**ISBN:** 9780521515924

**Category:** Mathematics

**Page:** 176

**View:** 5477

This simple, compact toolkit for designing and analyzing stochastic approximation algorithms requires only a basic understanding of probability and differential equations. Although powerful, these algorithms have applications in control and communications engineering, artificial intelligence and economic modeling. Unique topics include finite-time behavior, multiple timescales and asynchronous implementation. There is a useful plethora of applications, each with concrete examples from engineering and economics. Notably it covers variants of stochastic gradient-based optimization schemes, fixed-point solvers, which are commonplace in learning algorithms for approximate dynamic programming, and some models of collective behavior.
*Polymerization, Crystallization, Manufacturing*

**Author**: Vincenzo Capasso

**Publisher:** Springer Science & Business Media

**ISBN:** 3642557716

**Category:** Mathematics

**Page:** 320

**View:** 9600

Polymers are substances made of macromolecules formed by thousands of atoms organized in one (homopolymers) or more (copolymers) groups that repeat themselves to form linear or branched chains, or lattice structures. The concept of polymer traces back to the years 1920's and is one of the most significant ideas of last century. It has given great impulse to indus try but also to fundamental research, including life sciences. Macromolecules are made of sm all molecules known as monomers. The process that brings monomers into polymers is known as polymerization. A fundamental contri bution to the industrial production of polymers, particularly polypropylene and polyethylene, is due to the Nobel prize winners Giulio Natta and Karl Ziegler. The ideas of Ziegler and Natta date back to 1954, and the process has been improved continuously over the years, particularly concerning the design and shaping of the catalysts. Chapter 1 (due to A. Fasano ) is devoted to a review of some results concerning the modelling of the Ziegler- Natta polymerization. The specific ex am pie is the production of polypropilene. The process is extremely complex and all studies with relevant mathematical contents are fairly recent, and several problems are still open.

**Author**: George Osipenko

**Publisher:** Springer

**ISBN:** 3540355952

**Category:** Mathematics

**Page:** 288

**View:** 2646

This book describes a family of algorithms for studying the global structure of systems. By a finite covering of the phase space we construct a directed graph with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used, among other things, to locate the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, and more.

**Author**: Leah Edelstein-Keshet

**Publisher:** SIAM

**ISBN:** 9780898719147

**Category:** Biology

**Page:** 586

**View:** 322

Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.

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