Attractor Dimension Estimates For Dynamical Systems Theory And Computation
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Attractor Dimension Estimates For Dynamical Systems Theory And Computation
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Author : Nikolay Kuznetsov
language : en
Publisher: Springer Nature
Release Date : 2020-07-02
Attractor Dimension Estimates For Dynamical Systems Theory And Computation written by Nikolay Kuznetsov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-02 with Computers categories.
This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.
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.
Artificial Intelligence Applications And Innovations
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Author : Ilias Maglogiannis
language : en
Publisher: Springer Nature
Release Date : 2021-06-22
Artificial Intelligence Applications And Innovations written by Ilias Maglogiannis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-22 with Computers categories.
This book constitutes the refereed proceedings of the 17th IFIP WG 12.5 International Conference on Artificial Intelligence Applications and Innovations, AIAI 2021, held virtually and in Hersonissos, Crete, Greece, in June 2021. The 50 full papers and 11 short papers presented were carefully reviewed and selected from 113 submissions. They cover a broad range of topics related to technical, legal, and ethical aspects of artificial intelligence systems and their applications and are organized in the following sections: adaptive modeling/ neuroscience; AI in biomedical applications; AI impacts/ big data; automated machine learning; autonomous agents; clustering; convolutional NN; data mining/ word counts; deep learning; fuzzy modeling; hyperdimensional computing; Internet of Things/ Internet of energy; machine learning; multi-agent systems; natural language; recommendation systems; sentiment analysis; and smart blockchain applications/ cybersecurity. Chapter “Improving the Flexibility of Production Scheduling in Flat Steel Production Through Standard and AI-based Approaches: Challenges and Perspective” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Modeling Nonlinear Dynamics From Equations And Data With Applications To Solids Fluids And Controls
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Author : George Haller
language : en
Publisher: SIAM
Release Date : 2025-05-20
Modeling Nonlinear Dynamics From Equations And Data With Applications To Solids Fluids And Controls written by George Haller and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-20 with Computers categories.
This concise text presents an introduction to the emerging area of reducing complex nonlinear differential equations or time-resolved data sets to spectral submanifolds (SSMs). SSMs are ubiquitous low-dimensional attracting invariant manifolds that can be constructed systematically, building on the spectral properties of the linear part of a nonlinear system. The internal dynamics within SSMs then serve as exact, low-dimensional models with which the full system evolution synchronizes exponentially fast. SSM-based model reduction has a solid mathematical foundation and hence is guaranteed to deliver accurate and predictive reduced-order models under a precise set of assumptions. This book introduces the foundations of SSM theory to the novice reader; reviews recent extensions of classic SSM results for the advanced reader; and illustrates the power of SSM reduction on a large collection of equation- and data-driven applications in fluid mechanics, solid mechanics, and control. This book is intended for graduate students, postdocs, faculty, and industrial researchers working in model reduction for nonlinear physical systems arising in solid mechanics, fluid dynamics, and control theory. It is appropriate for courses on differential equations, modeling, dynamical systems, and data-driven modeling.
From Topology To Computation Proceedings Of The Smalefest
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Author : Morris W. Hirsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
From Topology To Computation Proceedings Of The Smalefest written by Morris W. Hirsch 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 2012-12-06 with Mathematics categories.
An extraordinary mathematical conference was held 5-9 August 1990 at the University of California at Berkeley: From Topology to Computation: Unity and Diversity in the Mathematical Sciences An International Research Conference in Honor of Stephen Smale's 60th Birthday The topics of the conference were some of the fields in which Smale has worked: • Differential Topology • Mathematical Economics • Dynamical Systems • Theory of Computation • Nonlinear Functional Analysis • Physical and Biological Applications This book comprises the proceedings of that conference. The goal of the conference was to gather in a single meeting mathemati cians working in the many fields to which Smale has made lasting con tributions. The theme "Unity and Diversity" is enlarged upon in the section entitled "Research Themes and Conference Schedule." The organizers hoped that illuminating connections between seemingly separate mathematical sub jects would emerge from the conference. Since such connections are not easily made in formal mathematical papers, the conference included discussions after each of the historical reviews of Smale's work in different fields. In addition, there was a final panel discussion at the end of the conference.
Handbook Of Dynamical Systems
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Author : B. Fiedler
language : en
Publisher: Gulf Professional Publishing
Release Date : 2002-02-21
Handbook Of Dynamical Systems written by B. Fiedler and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-02-21 with Science categories.
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.
Discrete And Continuous Dynamical Systems
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Author :
language : en
Publisher:
Release Date : 2008
Discrete And Continuous Dynamical Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Differentiable dynamical systems categories.
Deep Learning In Multi Step Prediction Of Chaotic Dynamics
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Author : Matteo Sangiorgio
language : en
Publisher: Springer Nature
Release Date : 2022-02-14
Deep Learning In Multi Step Prediction Of Chaotic Dynamics written by Matteo Sangiorgio and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-14 with Mathematics categories.
The book represents the first attempt to systematically deal with the use of deep neural networks to forecast chaotic time series. Differently from most of the current literature, it implements a multi-step approach, i.e., the forecast of an entire interval of future values. This is relevant for many applications, such as model predictive control, that requires predicting the values for the whole receding horizon. Going progressively from deterministic models with different degrees of complexity and chaoticity to noisy systems and then to real-world cases, the book compares the performances of various neural network architectures (feed-forward and recurrent). It also introduces an innovative and powerful approach for training recurrent structures specific for sequence-to-sequence tasks. The book also presents one of the first attempts in the context of environmental time series forecasting of applying transfer-learning techniques such as domain adaptation.
Ergodic Theory Analysis And Efficient Simulation Of Dynamical Systems
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Author : Bernold Fiedler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ergodic Theory Analysis And Efficient Simulation Of Dynamical Systems written by Bernold Fiedler 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 2012-12-06 with Mathematics categories.
This book summarizes and highlights progress in our understanding of Dy namical Systems during six years of the German Priority Research Program "Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems" . The program was funded by the Deutsche Forschungsgemeinschaft (DFG) and aimed at combining, focussing, and enhancing research efforts of active groups in the field by cooperation on a federal level. The surveys in the book are addressed to experts and non-experts in the mathematical community alike. In addition they intend to convey the significance of the results for applications far into the neighboring disciplines of Science. Three fundamental topics in Dynamical Systems are at the core of our research effort: behavior for large time dimension measure, and chaos Each of these topics is, of course, a highly complex problem area in itself and does not fit naturally into the deplorably traditional confines of any of the disciplines of ergodic theory, analysis, or numerical analysis alone. The necessity of mathematical cooperation between these three disciplines is quite obvious when facing the formidahle task of establishing a bidirectional transfer which bridges the gap between deep, detailed theoretical insight and relevant, specific applications. Both analysis and numerical analysis playa key role when it comes to huilding that bridge. Some steps of our joint bridging efforts are collected in this volume. Neither our approach nor the presentations in this volume are monolithic.
Soviet Physics
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Author :
language : en
Publisher:
Release Date : 1990
Soviet Physics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Physics categories.