An Introduction To Piecewise Smooth Dynamics

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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.

An Introduction to Piecewise Smooth Dynamics

Author : Paul Glendinning
Publisher : Springer Nature
ISBN 13 : 3030236897
Total Pages : 134 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis An Introduction to Piecewise Smooth Dynamics by : Paul Glendinning

Download or read book An Introduction to Piecewise Smooth Dynamics written by Paul Glendinning and published by Springer Nature. This book was released on 2019-10-21 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at mathematicians, scientists, and engineers, studying models that involve a discontinuity, or studying the theory of nonsmooth systems for its own sake. It is divided in two complementary courses: piecewise smooth flows and maps, respectively. Starting from well known theoretical results, the authors bring the reader into the latest challenges in the field, going through stability analysis, bifurcation, singularities, decomposition theorems and an introduction to kneading theory. Both courses contain many examples which illustrate the theoretical concepts that are introduced.

Bifurcations in Piecewise-smooth Continuous Systems

Author : David John Warwick Simpson
Publisher : World Scientific
ISBN 13 : 9814293849
Total Pages : 255 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Bifurcations in Piecewise-smooth Continuous Systems by : David John Warwick Simpson

Download or read book Bifurcations in Piecewise-smooth Continuous Systems written by David John Warwick Simpson and published by World Scientific. This book was released on 2010 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail. NeimarkSacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems.

Introduction to the Modern Theory of Dynamical Systems

Author : Anatole Katok
Publisher : Cambridge University Press
ISBN 13 : 9780521575577
Total Pages : 828 pages
Book Rating : 4.5/5 (755 download)

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Book Synopsis Introduction to the Modern Theory of Dynamical Systems by : Anatole Katok

Download or read book Introduction to the Modern Theory of Dynamical Systems written by Anatole Katok and published by Cambridge University Press. This book was released on 1995 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.

Extended Abstracts Spring 2016

Author : Alessandro Colombo
Publisher : Birkhäuser
ISBN 13 : 3319556428
Total Pages : 187 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Extended Abstracts Spring 2016 by : Alessandro Colombo

Download or read book Extended Abstracts Spring 2016 written by Alessandro Colombo and published by Birkhäuser. This book was released on 2017-05-24 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the "Intensive Research Program on Advances in Nonsmooth Dynamics 2016", held at the Centre de Recerca Matemàtica (CRM) in Barcelona from February 1st to April 29th, 2016. They include brief research articles reporting new results, descriptions of preliminary work or open problems, and outlines of prominent discussion sessions. The articles are all the result of direct collaborations initiated during the research program. The topic is the theory and applications of Nonsmooth Dynamics. This includes systems involving elements of: impacting, switching, on/off control, hybrid discrete-continuous dynamics, jumps in physical properties, and many others. Applications include: electronics, climate modeling, life sciences, mechanics, ecology, and more. Numerous new results are reported concerning the dimensionality and robustness of nonsmooth models, shadowing variables, numbers of limit cycles, discontinuity-induced bifurcations and chaos, determinacy-breaking, stability criteria, and the classification of attractors and other singularities. This material offers a variety of new exciting problems to mathematicians, but also a diverse range of new tools and insights for scientists and engineers making use of mathematical modeling and analysis. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Author : John Guckenheimer
Publisher : Springer Science & Business Media
ISBN 13 : 1461211409
Total Pages : 475 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by : John Guckenheimer

Download or read book Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields written by John Guckenheimer and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Bifurcations and Chaos in Piecewise-smooth Dynamical Systems

Author : Zhanybai T. Zhusubaliyev
Publisher : World Scientific
ISBN 13 : 9812384200
Total Pages : 377 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Bifurcations and Chaos in Piecewise-smooth Dynamical Systems by : Zhanybai T. Zhusubaliyev

Download or read book Bifurcations and Chaos in Piecewise-smooth Dynamical Systems written by Zhanybai T. Zhusubaliyev and published by World Scientific. This book was released on 2003 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.

Modeling with Nonsmooth Dynamics

Author : Mike R. Jeffrey
Publisher : Springer Nature
ISBN 13 : 3030359875
Total Pages : 104 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Modeling with Nonsmooth Dynamics by : Mike R. Jeffrey

Download or read book Modeling with Nonsmooth Dynamics written by Mike R. Jeffrey and published by Springer Nature. This book was released on 2020-02-22 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume looks at the study of dynamical systems with discontinuities. Discontinuities arise when systems are subject to switches, decisions, or other abrupt changes in their underlying properties that require a ‘non-smooth’ definition. A review of current ideas and introduction to key methods is given, with a view to opening discussion of a major open problem in our fundamental understanding of what nonsmooth models are. What does a nonsmooth model represent: an approximation, a toy model, a sophisticated qualitative capturing of empirical law, or a mere abstraction? Tackling this question means confronting rarely discussed indeterminacies and ambiguities in how we define, simulate, and solve nonsmooth models. The author illustrates these with simple examples based on genetic regulation and investment games, and proposes precise mathematical tools to tackle them. The volume is aimed at students and researchers who have some experience of dynamical systems, whether as a modelling tool or studying theoretically. Pointing to a range of theoretical and applied literature, the author introduces the key ideas needed to tackle nonsmooth models, but also shows the gaps in understanding that all researchers should be bearing in mind. Mike Jeffrey is a researcher and lecturer at the University of Bristol with a background in mathematical physics, specializing in dynamics, singularities, and asymptotics.

Hidden Dynamics

Author : Mike R. Jeffrey
Publisher : Springer
ISBN 13 : 3030021076
Total Pages : 531 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Hidden Dynamics by : Mike R. Jeffrey

Download or read book Hidden Dynamics written by Mike R. Jeffrey and published by Springer. This book was released on 2018-12-11 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dream of mathematical modeling is of systems evolving in a continuous, deterministic, predictable way. Unfortunately continuity is lost whenever the `rules of the game' change, whether a change of behavioural regime, or a change of physical properties. From biological mitosis to seizures. From rattling machine parts to earthquakes. From individual decisions to economic crashes. Where discontinuities occur, determinacy is inevitably lost. Typically the physical laws of such change are poorly understood, and too ill-defined for standard mathematics. Discontinuities offer a way to make the bounds of scientific knowledge a part of the model, to analyse a system with detail and rigour, yet still leave room for uncertainty. This is done without recourse to stochastic modeling, instead retaining determinacy as far as possible, and focussing on the geometry of the many outcomes that become possible when it breaks down. In this book the foundations of `piecewise-smooth dynamics' theory are rejuvenated, given new life through the lens of modern nonlinear dynamics and asymptotics. Numerous examples and exercises lead the reader through from basic to advanced analytical methods, particularly new tools for studying stability and bifurcations. The book is aimed at scientists and engineers from any background with a basic grounding in calculus and linear algebra. It seeks to provide an invaluable resource for modeling discontinuous systems, but also to empower the reader to develop their own novel models and discover as yet unknown phenomena.

Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems

Author : Luis Rodrigues
Publisher : SIAM
ISBN 13 : 1611975905
Total Pages : 243 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems by : Luis Rodrigues

Download or read book Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems written by Luis Rodrigues and published by SIAM. This book was released on 2019-11-06 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements. The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications. Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.

Handbook of Dynamical Systems

Author : B. Fiedler
Publisher : Gulf Professional Publishing
ISBN 13 : 0080532845
Total Pages : 1099 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Dynamical Systems by : B. Fiedler

Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures

Author : Viktor Avrutin
Publisher : World Scientific
ISBN 13 : 9811204713
Total Pages : 649 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures by : Viktor Avrutin

Download or read book Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures written by Viktor Avrutin and published by World Scientific. This book was released on 2019-05-28 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.

Introduction to Applied Linear Algebra

Author : Stephen Boyd
Publisher : Cambridge University Press
ISBN 13 : 1316518965
Total Pages : 477 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd

Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

One-Dimensional Dynamics

Author : Welington de Melo
Publisher : Springer Science & Business Media
ISBN 13 : 3642780431
Total Pages : 616 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis One-Dimensional Dynamics by : Welington de Melo

Download or read book One-Dimensional Dynamics written by Welington de Melo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).

Chaotic Systems with Multistability and Hidden Attractors

Author : Xiong Wang
Publisher : Springer Nature
ISBN 13 : 3030758214
Total Pages : 661 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Chaotic Systems with Multistability and Hidden Attractors by : Xiong Wang

Download or read book Chaotic Systems with Multistability and Hidden Attractors written by Xiong Wang and published by Springer Nature. This book was released on 2021-12-01 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of new articles written by world-leading experts and active researchers to present their recent finding and progress in the new area of chaotic systems and dynamics, regarding emerging subjects of unconventional chaotic systems and their complex dynamics.It guide readers directly to the research front of the new scientific studies. This book is unique of its kind in the current literature, presenting broad scientific research topics including multistability and hidden attractors in unconventional chaotic systems, such as chaotic systems without equilibria, with only stable equilibria, with a curve or a surface of equilibria. The book describes many novel phenomena observed from chaotic systems, such as non-Shilnikov type chaos, coexistence of different types of attractors, and spontaneous symmetry breaking in chaotic systems. The book presents state-of-the-art scientific research progress in the field with both theoretical advances and potential applications. This book is suitable for all researchers and professionals in the areas of nonlinear dynamics and complex systems, including research professionals, physicists, applied mathematicians, computer scientists and, in particular, graduate students in related fields.

Feedback Systems

Author : Karl Johan Åström
Publisher : Princeton University Press
ISBN 13 : 069121347X
Total Pages : pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Feedback Systems by : Karl Johan Åström

Download or read book Feedback Systems written by Karl Johan Åström and published by Princeton University Press. This book was released on 2021-02-02 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory

Advances in Mathematics and Applications

Author : Carlile Lavor
Publisher : Springer
ISBN 13 : 3319940155
Total Pages : 408 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Advances in Mathematics and Applications by : Carlile Lavor

Download or read book Advances in Mathematics and Applications written by Carlile Lavor and published by Springer. This book was released on 2018-09-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book celebrates the 50th anniversary of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the University of Campinas, Brazil, by offering reviews of selected research developed at one of the most prestigious mathematics institutes in Latin America. Written by senior professors at the IMECC, it covers topics in pure and applied mathematics and statistics ranging from differential geometry, dynamical systems, Lie groups, and partial differential equations to computational optimization, mathematical physics, stochastic process, time series, and more. A report on the challenges and opportunities of research in applied mathematics - a highly active field of research in the country - and highlights of the Institute since its foundation in 1968 completes this historical volume, which is unveiled in the same year that the International Mathematical Union (IMU) names Brazil as a member of the Group V of countries with the most relevant contributions in mathematics.