Numerical Methods For Nonsmooth Dynamical Systems

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Numerical Methods for Nonsmooth Dynamical Systems

Author : Vincent Acary
Publisher : Springer Science & Business Media
ISBN 13 : 3540753923
Total Pages : 529 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Numerical Methods for Nonsmooth Dynamical Systems by : Vincent Acary

Download or read book Numerical Methods for Nonsmooth Dynamical Systems written by Vincent Acary and published by Springer Science & Business Media. This book was released on 2008-01-30 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonsmooth Mechanics

Author : Bernard Brogliato
Publisher : Springer Science & Business Media
ISBN 13 : 1447105575
Total Pages : 565 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Nonsmooth Mechanics by : Bernard Brogliato

Download or read book Nonsmooth Mechanics written by Bernard Brogliato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.

Piecewise-smooth Dynamical Systems

Author : Mario Bernardo
Publisher : Springer Science & Business Media
ISBN 13 : 1846287081
Total Pages : 497 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Piecewise-smooth Dynamical Systems by : Mario Bernardo

Download or read book Piecewise-smooth Dynamical Systems written by Mario Bernardo and published by Springer Science & Business Media. This book was released on 2008-01-01 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.

Bifurcation and Chaos in Nonsmooth Mechanical Systems

Author : Jan Awrejcewicz
Publisher : World Scientific
ISBN 13 : 9812384596
Total Pages : 564 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Bifurcation and Chaos in Nonsmooth Mechanical Systems by : Jan Awrejcewicz

Download or read book Bifurcation and Chaos in Nonsmooth Mechanical Systems written by Jan Awrejcewicz and published by World Scientific. This book was released on 2003 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.

Nonsmooth Modeling and Simulation for Switched Circuits

Author : Vincent Acary
Publisher : Springer Science & Business Media
ISBN 13 : 9048196817
Total Pages : 295 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis Nonsmooth Modeling and Simulation for Switched Circuits by : Vincent Acary

Download or read book Nonsmooth Modeling and Simulation for Switched Circuits written by Vincent Acary and published by Springer Science & Business Media. This book was released on 2010-10-19 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth Modeling and Simulation for Switched Circuits concerns the modeling and the numerical simulation of switched circuits with the nonsmooth dynamical systems (NSDS) approach, using piecewise-linear and multivalued models of electronic devices like diodes, transistors, switches. Numerous examples (ranging from introductory academic circuits to various types of power converters) are analyzed and many simulation results obtained with the INRIA open-source SICONOS software package are presented. Comparisons with SPICE and hybrid methods demonstrate the power of the NSDS approach. Nonsmooth Modeling and Simulation for Switched Circuits is intended to researchers and engineers in the field of circuits simulation and design, but may also attract applied mathematicians interested by the numerical analysis for nonsmooth dynamical systems, as well as researchers from Systems and Control.

Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Author : Remco I. Leine
Publisher : Springer Science & Business Media
ISBN 13 : 3540443983
Total Pages : 245 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Dynamics and Bifurcations of Non-Smooth Mechanical Systems by : Remco I. Leine

Download or read book Dynamics and Bifurcations of Non-Smooth Mechanical Systems written by Remco I. Leine and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Dynamical Systems Method and Applications

Author : Alexander G. Ramm
Publisher : John Wiley & Sons
ISBN 13 : 111819960X
Total Pages : 522 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis Dynamical Systems Method and Applications by : Alexander G. Ramm

Download or read book Dynamical Systems Method and Applications written by Alexander G. Ramm and published by John Wiley & Sons. This book was released on 2013-06-07 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and then sets forth the scope of DSM in Part One. Part Two introduces the discrepancy principle, and Part Three offers examples of numerical applications of DSM to solve a broad range of problems in science and engineering. Additional featured topics include: General nonlinear operator equations Operators satisfying a spectral assumption Newton-type methods without inversion of the derivative Numerical problems arising in applications Stable numerical differentiation Stable solution to ill-conditioned linear algebraic systems Throughout the chapters, the authors employ the use of figures and tables to help readers grasp and apply new concepts. Numerical examples offer original theoretical results based on the solution of practical problems involving ill-conditioned linear algebraic systems, and stable differentiation of noisy data. Written by internationally recognized authorities on the topic, Dynamical Systems Method and Applications is an excellent book for courses on numerical analysis, dynamical systems, operator theory, and applied mathematics at the graduate level. The book also serves as a valuable resource for professionals in the fields of mathematics, physics, and engineering.

Advanced Topics in Nonsmooth Dynamics

Author : Remco Leine
Publisher : Springer
ISBN 13 : 3319759728
Total Pages : 462 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Advanced Topics in Nonsmooth Dynamics by : Remco Leine

Download or read book Advanced Topics in Nonsmooth Dynamics written by Remco Leine and published by Springer. This book was released on 2018-06-07 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses emerging topics in the area of nonsmooth dynamics research, such as numerical methods for nonsmooth systems, impact laws for multi-collisions, nonlinear vibrations and control of nonsmooth systems. It documents original work of researchers at the European Network for NonSmooth Dynamics (ENNSD), which provides a cooperation platform for researchers in the field and promotes research focused on nonsmooth dynamics and its applications. Since the establishment of the network in 2012, six ENNSD symposia have been organized at different European locations. The network brings together 40 specialists from 9 different countries in and outside Europe and a wealth of scientific knowledge has been gathered and developed by this group of experts in recent years. The book is of interest to both new and experienced researchers in the field of nonsmooth dynamics. Each chapter is written in such a way as to provide an introduction to the topic for researchers from other fields.

Nonsmooth Mechanics

Author : Bernard Brogliato
Publisher : Springer
ISBN 13 : 3319286641
Total Pages : 657 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Nonsmooth Mechanics by : Bernard Brogliato

Download or read book Nonsmooth Mechanics written by Bernard Brogliato and published by Springer. This book was released on 2016-02-29 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to issues connected with control and modelling. It covers Lagrangian and Newton–Euler systems, detailing mathematical tools such as convex analysis and complementarity theory. The ways in which nonsmooth mechanics influence and are influenced by well-posedness analysis, numerical analysis and simulation, modelling and control are explained. Contact/impact laws, stability theory and trajectory-tracking control are given detailed exposition connected by a mathematical framework formed from complementarity systems and measure-differential inclusions. Links are established with electrical circuits with set-valued nonsmooth elements as well as with other nonsmooth dynamical systems like impulsive and piecewise linear systems. Nonsmooth Mechanics (third edition) retains the topical structure familiar from its predecessors but has been substantially rewritten, edited and updated to account for the significant body of results that have emerged in the twenty-first century—including developments in: the existence and uniqueness of solutions; impact models; extension of the Lagrange–Dirichlet theorem and trajectory tracking; and well-posedness of contact complementarity problems with and without friction. Many figures (both new and redrawn to improve the clarity of the presentation) and examples are used to illustrate the theoretical developments. Material introducing the mathematics of nonsmooth mechanics has been improved to reflect the broad range of applications interest that has developed since publication of the second edition. The detail of some mathematical essentials is provided in four appendices. With its improved bibliography of over 1,300 references and wide-ranging coverage, Nonsmooth Mechanics (third edition) is sure to be an invaluable resource for researchers and postgraduates studying the control of mechanical systems, robotics, granular matter and relevant fields of applied mathematics. “The book’s two best features, in my view are its detailed survey of the literature... and its detailed presentation of many examples illustrating both the techniques and their limitations... For readers interested in the field, this book will serve as an excellent introductory survey.” Andrew Lewis in Automatica “It is written with clarity, contains the latest research results in the area of impact problems for rigid bodies and is recommended for both applied mathematicians and engineers.” Panagiotis D. Panagiotopoulos in Mathematical Reviews “The presentation is excellent in combining rigorous mathematics with a great number of examples... allowing the reader to understand the basic concepts.” Hans Troger in Mathematical Abstracts “/i>

Elliptic Problems in Nonsmooth Domains

Author : Pierre Grisvard
Publisher : SIAM
ISBN 13 : 1611972027
Total Pages : 426 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Elliptic Problems in Nonsmooth Domains by : Pierre Grisvard

Download or read book Elliptic Problems in Nonsmooth Domains written by Pierre Grisvard and published by SIAM. This book was released on 2011-10-20 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: Boston: Pitman Advanced Pub. Program, 1985.

Smooth and Nonsmooth High Dimensional Chaos and the Melnikov-Type Methods

Author : Jan Awrejcewicz
Publisher : World Scientific
ISBN 13 : 981270910X
Total Pages : 318 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Smooth and Nonsmooth High Dimensional Chaos and the Melnikov-Type Methods by : Jan Awrejcewicz

Download or read book Smooth and Nonsmooth High Dimensional Chaos and the Melnikov-Type Methods written by Jan Awrejcewicz and published by World Scientific. This book was released on 2007 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in the case of mechanics, they represent one-degree-of-freedom nonautonomous systems). This book extends the classical Melnikov's approach to the study of high dimensional dynamical systems, and uses simple models of dry friction to analytically predict the occurrence of both stick-slip and slip-slip chaotic orbits, research which is very rarely reported in the existing literature even on one-degree-of-freedom nonautonomous dynamics. This pioneering attempt to predict the occurrence of deterministic chaos of nonlinear dynamical systems will attract many researchers including applied mathematicians, physicists, as well as practicing engineers. Analytical formulas are explicitly formulated step-by-step, even attracting potential readers without a rigorous mathematical background. Sample Chapter(s). Chapter 1: A Role of the Melnikov-Type Methods in Applied Sciences (137 KB). Contents: A Role of the Melnikov-Type Methods in Applied Sciences; Classical Melnikov Approach; Homoclinic Chaos Criterion in a Rotated Froude Pendulum with Dry Friction; Smooth and Nonsmooth Dynamics of a Quasi-Autonomous Oscillator with Coulomb and Viscous Frictions; Application of the MelnikovOCoGruendler Method to Mechanical Systems; A Self-Excited Spherical Pendulum; A Double Self-excited Duffing-type Oscillator; A Triple Self-Excited Duffing-type Oscillator. Readership: Graduate students and researchers in dynamical systems.

Non-Smooth Deterministic or Stochastic Discrete Dynamical Systems

Author : Jerome Bastien
Publisher : John Wiley & Sons
ISBN 13 : 1118604083
Total Pages : 514 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Non-Smooth Deterministic or Stochastic Discrete Dynamical Systems by : Jerome Bastien

Download or read book Non-Smooth Deterministic or Stochastic Discrete Dynamical Systems written by Jerome Bastien and published by John Wiley & Sons. This book was released on 2013-03-18 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains theoretical and application-oriented methods to treat models of dynamical systems involving non-smooth nonlinearities. The theoretical approach that has been retained and underlined in this work is associated with differential inclusions of mainly finite dimensional dynamical systems and the introduction of maximal monotone operators (graphs) in order to describe models of impact or friction. The authors of this book master the mathematical, numerical and modeling tools in a particular way so that they can propose all aspects of the approach, in both a deterministic and stochastic context, in order to describe real stresses exerted on physical systems. Such tools are very powerful for providing reference numerical approximations of the models. Such an approach is still not very popular nevertheless, even though it could be very useful for many models of numerous fields (e.g. mechanics, vibrations, etc.). This book is especially suited for people both in research and industry interested in the modeling and numerical simulation of discrete mechanical systems with friction or impact phenomena occurring in the presence of classical (linear elastic) or non-classical constitutive laws (delay, memory effects, etc.). It aims to close the gap between highly specialized mathematical literature and engineering applications, as well as to also give tools in the framework of non-smooth stochastic differential systems: thus, applications involving stochastic excitations (earthquakes, road surfaces, wind models etc.) are considered. Contents 1. Some Simple Examples. 2. Theoretical Deterministic Context. 3. Stochastic Theoretical Context. 4. Riemannian Theoretical Context. 5. Systems with Friction. 6. Impact Systems. 7. Applications–Extensions. About the Authors Jérôme Bastien is Assistant Professor at the University Lyon 1 (Centre de recherche et d'Innovation sur le sport) in France. Frédéric Bernardin is a Research Engineer at Département Laboratoire de Clermont-Ferrand (DLCF), Centre d'Etudes Techniques de l'Equipement (CETE), Lyon, France. Claude-Henri Lamarque is Head of Laboratoire Géomatériaux et Génie Civil (LGCB) and Professor at Ecole des Travaux Publics de l'Etat (ENTPE), Vaulx-en-Velin, France.

Impulsive and Hybrid Dynamical Systems

Author : Wassim M. Haddad
Publisher : Princeton University Press
ISBN 13 : 1400865247
Total Pages : 522 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Impulsive and Hybrid Dynamical Systems by : Wassim M. Haddad

Download or read book Impulsive and Hybrid Dynamical Systems written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2014-09-08 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems. Such a framework is imperative for modern complex engineering systems that involve interacting continuous-time and discrete-time dynamics with multiple modes of operation that place stringent demands on controller design and require implementation of increasing complexity--whether advanced high-performance tactical fighter aircraft and space vehicles, variable-cycle gas turbine engines, or air and ground transportation systems. Impulsive and Hybrid Dynamical Systems goes beyond similar treatments by developing invariant set stability theorems, partial stability, Lagrange stability, boundedness, ultimate boundedness, dissipativity theory, vector dissipativity theory, energy-based hybrid control, optimal control, disturbance rejection control, and robust control for nonlinear impulsive and hybrid dynamical systems. A major contribution to mathematical system theory and control system theory, this book is written from a system-theoretic point of view with the highest standards of exposition and rigor. It is intended for graduate students, researchers, and practitioners of engineering and applied mathematics as well as computer scientists, physicists, and other scientists who seek a fundamental understanding of the rich dynamical behavior of impulsive and hybrid dynamical systems.

A Variational Approach to Nonsmooth Dynamics

Author : Samir Adly
Publisher : Springer
ISBN 13 : 3319686585
Total Pages : 168 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis A Variational Approach to Nonsmooth Dynamics by : Samir Adly

Download or read book A Variational Approach to Nonsmooth Dynamics written by Samir Adly and published by Springer. This book was released on 2018-02-19 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief examines mathematical models in nonsmooth mechanics and nonregular electrical circuits, including evolution variational inequalities, complementarity systems, differential inclusions, second-order dynamics, Lur'e systems and Moreau's sweeping process. The field of nonsmooth dynamics is of great interest to mathematicians, mechanicians, automatic controllers and engineers. The present volume acknowledges this transversality and provides a multidisciplinary view as it outlines fundamental results in nonsmooth dynamics and explains how to use them to study various problems in engineering. In particular, the author explores the question of how to redefine the notion of dynamical systems in light of modern variational and nonsmooth analysis. With the aim of bridging between the communities of applied mathematicians, engineers and researchers in control theory and nonlinear systems, this brief outlines both relevant mathematical proofs and models in unilateral mechanics and electronics.

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

Author : Michal Feckan
Publisher : Academic Press
ISBN 13 : 0128043644
Total Pages : 262 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems by : Michal Feckan

Download or read book Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems written by Michal Feckan and published by Academic Press. This book was released on 2016-06-07 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions. The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincaré mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity. - Extends Melnikov analysis of the classic Poincaré and Andronov staples, pointing to a general theory for freedom in dimensions of spatial variables and parameters as well as asymptotical results such as stability, instability, and hyperbolicity - Presents a toolbox of critical theoretical techniques for many practical examples and models, including non-smooth dynamical systems - Provides realistic models based on unsolved discontinuous problems from the literature and describes how Poincaré-Andronov-Melnikov analysis can be used to solve them - Investigates the relationship between non-smooth systems and their continuous approximations

Numerical Methods for Conservation Laws

Author : LEVEQUE
Publisher : Birkhäuser
ISBN 13 : 3034851162
Total Pages : 221 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Numerical Methods for Conservation Laws by : LEVEQUE

Download or read book Numerical Methods for Conservation Laws written by LEVEQUE and published by Birkhäuser. This book was released on 2013-11-11 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.

Projected Dynamical Systems and Variational Inequalities with Applications

Author : Anna Nagurney
Publisher : Springer Science & Business Media
ISBN 13 : 146152301X
Total Pages : 312 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Projected Dynamical Systems and Variational Inequalities with Applications by : Anna Nagurney

Download or read book Projected Dynamical Systems and Variational Inequalities with Applications written by Anna Nagurney and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equilibrium is a concept used in operations research and economics to understand the interplay of factors and problems arising from competitive systems in the economic world. The problems in this area are large and complex and have involved a variety of mathematical methodologies. In this monograph, the authors have widened the scope of theoretical work with a new approach, `projected dynamical systems theory', to previous work in variational inequality theory. While most classical work in this area is static, the introduction to the theory of projected dynamical systems will allow many real-life dynamic situations and problems to be handled and modeled. This monograph includes: a new theoretical approach, `projected dynamical system', which allows the researcher to model real-life situations more accurately; new mathematical methods allowing researchers to combine other theoretical approaches with the projected dynamical systems approach; a framework in which research can adequately model natural, financial and human (real life) situations in competitive equilibrium problems; the computational and numerical methods for the implementation of the methods and theory discussed in the book; stability analysis, algorithms and computational procedures are offered for each set of applications.