Author: Mario Bernardo
Publisher: Springer Science & Business Media
ISBN: 1846287081
Category : Mathematics
Languages : en
Pages : 497
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Book Description
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.
Author: Markus Kunze
Publisher: Springer
ISBN: 9783662206102
Category :
Languages : en
Pages : 244
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Book Description
The book provides a self-contained introduction to the mathematical theory of non-smooth dynamical problems, as they frequently arise from mechanical systems with friction and/or impacts. It is aimed at applied mathematicians, engineers, and applied scientists in general who wish to learn the subject.
Author: M. C. Irwin
Publisher: World Scientific
ISBN: 9810245998
Category : Mathematics
Languages : en
Pages : 273
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Book Description
This is a reprint of M C Irwin's beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area.
Author: Michael Charles Irwin
Publisher: World Scientific
ISBN: 9789812810120
Category : Mathematics
Languages : en
Pages : 280
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Book Description
This is a reprint of M C Irwin''s beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area. Request Inspection Copy. Contents: Some Simple Examples; Equivalent Systems; Integration of Vector Fields; Linear Systems, Linearization, Stable Manifolds; Stable Systems; Appendices. Readership: Graduate students in mathematics.
Author: Remco I. Leine
Publisher: Springer Science & Business Media
ISBN: 3540443983
Category : Mathematics
Languages : en
Pages : 245
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Book Description
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.
Author: Pei-Dong Liu
Publisher: Springer
ISBN: 3540492917
Category : Mathematics
Languages : en
Pages : 233
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Book Description
This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.
Author: James D. Meiss
Publisher: SIAM
ISBN: 161197464X
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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: Vincent Acary
Publisher: Springer Science & Business Media
ISBN: 3540753923
Category : Technology & Engineering
Languages : en
Pages : 529
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Book Description
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: Ludwig Arnold
Publisher: Springer Science & Business Media
ISBN: 3662128780
Category : Mathematics
Languages : en
Pages : 590
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Book Description
The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.
Author: Jürgen Jost
Publisher: Springer Science & Business Media
ISBN: 3540288899
Category : Science
Languages : en
Pages : 199
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Book Description
Breadth of scope is unique Author is a widely-known and successful textbook author Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples Includes a section on cellular automata
