An Introduction To Piecewise Smooth Dynamics
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An Introduction To Piecewise Smooth Dynamics
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Author : Paul Glendinning
language : en
Publisher: Springer Nature
Release Date : 2019-10-21
An Introduction To Piecewise Smooth Dynamics written by Paul Glendinning and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-21 with Mathematics categories.
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.
Piecewise Smooth Dynamical Systems
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Author : Mario Bernardo
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-01
Piecewise Smooth Dynamical Systems written by Mario Bernardo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
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.
Piecewise Smooth Dynamical Systems
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Author : Mario Bernardo
language : en
Publisher: Springer
Release Date : 2008-01-15
Piecewise Smooth Dynamical Systems written by Mario Bernardo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-15 with Mathematics categories.
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 The Theory Of Smooth Dynamical Systems
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Author : W. Szlenk
language : en
Publisher:
Release Date : 1984
An Introduction To The Theory Of Smooth Dynamical Systems written by W. Szlenk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
This book is aimed at readers who are familiar with a standard undergraduate course of mathematics. It forms a short account of the main ideas and results in the theory of smooth dynamical systems.
Continuous And Discontinuous Piecewise Smooth One Dimensional Maps Invariant Sets And Bifurcation Structures
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Author : Gardini Laura
language : en
Publisher: World Scientific
Release Date : 2019-05-28
Continuous And Discontinuous Piecewise Smooth One Dimensional Maps Invariant Sets And Bifurcation Structures written by Gardini Laura and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-28 with Mathematics categories.
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.
Bifurcations In Piecewise Smooth Continuous Systems
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Author : David John Warwick Simpson
language : en
Publisher: World Scientific
Release Date : 2010
Bifurcations In Piecewise Smooth Continuous Systems written by David John Warwick Simpson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
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.
Bifurcations And Chaos In Piecewise Smooth Dynamical Systems
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Author : Zhanybai T. Zhusubaliyev
language : en
Publisher: World Scientific
Release Date : 2003
Bifurcations And Chaos In Piecewise Smooth Dynamical Systems written by Zhanybai T. Zhusubaliyev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Technical problems often lead to differential equations withpiecewise-smooth right-hand sides. Problems in mechanicalengineering, for instance, violate the requirements of smoothness ifthey involve collisions, finite clearances, or stickOCoslipphenomena."
Modeling With Nonsmooth Dynamics
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Author : Mike R. Jeffrey
language : en
Publisher: Springer Nature
Release Date : 2020-02-22
Modeling With Nonsmooth Dynamics written by Mike R. Jeffrey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-22 with Mathematics categories.
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.
Chaotic Systems With Multistability And Hidden Attractors
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Author : Xiong Wang
language : en
Publisher: Springer Nature
Release Date : 2021-12-01
Chaotic Systems With Multistability And Hidden Attractors written by Xiong Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-01 with Technology & Engineering categories.
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.
Hidden Dynamics
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Author : Mike R. Jeffrey
language : en
Publisher: Springer
Release Date : 2018-12-11
Hidden Dynamics written by Mike R. Jeffrey and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-11 with Mathematics categories.
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.