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Regularity and Complexity in Dynamical Systems

Author : Albert C. J. Luo

Publisher : Springer Science & Business Media

Page : 500 pages

File Size : 48,42 MB

Release : 2013-07-12

Category : Mathematics

ISBN : 1461415233

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Book Description

Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.



Regularity and Complexity in Dynamical Systems

Author : Albert C. J. Luo

Publisher : Springer Science & Business Media

Page : 503 pages

File Size : 21,74 MB

Release : 2011-12-21

Category : Technology & Engineering

ISBN : 1461415241

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Book Description

Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.





Permutation Complexity in Dynamical Systems

Author : José Amigó

Publisher : Springer Science & Business Media

Page : 260 pages

File Size : 17,13 MB

Release : 2010-03-20

Category : Science

ISBN : 3642040845

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Book Description

The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods, while periodicity is not. Another interesting feature is that since it can be shown that random (unconstrained) dynamics has no forbidden patterns with probability one, their existence can be used as a fingerprint to identify any deterministic origin of orbit generation. This book is primarily addressed to researchers working in the field of nonlinear dynamics and complex systems, yet will also be suitable for graduate students interested in these subjects. The presentation is a compromise between mathematical rigor and pedagogical approach. Accordingly, some of the more mathematical background needed for more in depth understanding has been shifted into the appendices.



Mathematics of Complexity and Dynamical Systems

Author : Robert A. Meyers

Publisher : Springer Science & Business Media

Page : 1885 pages

File Size : 41,14 MB

Release : 2011-10-05

Category : Mathematics

ISBN : 1461418054

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Book Description

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.



Assessing Complexity in Physiological Systems through Biomedical Signals Analysis

Author : Paolo Castiglioni

Publisher : MDPI

Page : 296 pages

File Size : 35,67 MB

Release : 2021-03-02

Category : Mathematics

ISBN : 3039433687

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Book Description

Complexity is a ubiquitous phenomenon in physiology that allows living systems to adapt to external perturbations. Fractal structures, self-organization, nonlinearity, interactions at different scales, and interconnections among systems through anatomical and functional networks, may originate complexity. Biomedical signals from physiological systems may carry information about the system complexity useful to identify physiological states, monitor health, and predict pathological events. Therefore, complexity analysis of biomedical signals is a rapidly evolving field aimed at extracting information on the physiological systems. This book consists of 16 contributions from authors with a strong scientific background in biomedical signals analysis. It includes reviews on the state-of-the-art of complexity studies in specific medical applications, new methods to improve complexity quantifiers, and novel complexity analyses in physiological or clinical scenarios. It presents a wide spectrum of methods investigating the entropic properties, multifractal structure, self-organized criticality, and information dynamics of biomedical signals touching upon three physiological areas: the cardiovascular system, the central nervous system, the heart-brain interactions. The book is aimed at experienced researchers in signal analysis and presents the latest trends in the complexity methods in physiology and medicine with the hope of inspiring future works advancing this fascinating area of research.



Handbook on Entropy, Complexity and Spatial Dynamics

Author : Reggiani, Aura

Publisher : Edward Elgar Publishing

Page : 640 pages

File Size : 35,6 MB

Release : 2021-12-14

Category : Social Science

ISBN : 1839100591

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Book Description

This ground-breaking Handbook presents a state-of-the-art exploration of entropy, complexity and spatial dynamics from fundamental theoretical, empirical and methodological perspectives. It considers how foundational theories can contribute to new advances, including novel modeling and empirical insights at different sectoral, spatial and temporal scales.



Feedback Systems

Author : Karl Johan Åström

Publisher : Princeton University Press

Page : pages

File Size : 10,90 MB

Release : 2021-02-02

Category : Technology & Engineering

ISBN : 069121347X

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Book Description

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



Dynamics in Action

Author : Alicia Juarrero

Publisher : MIT Press

Page : 306 pages

File Size : 22,23 MB

Release : 2002-01-25

Category : Psychology

ISBN : 9780262600477

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Book Description

What is the difference between a wink and a blink? The answer is important not only to philosophers of mind, for significant moral and legal consequences rest on the distinction between voluntary and involuntary behavior. However, "action theory"—the branch of philosophy that has traditionally articulated the boundaries between action and non-action, and between voluntary and involuntary behavior—has been unable to account for the difference. Alicia Juarrero argues that a mistaken, 350-year-old model of cause and explanation—one that takes all causes to be of the push-pull, efficient cause sort, and all explanation to be prooflike—underlies contemporary theories of action. Juarrero then proposes a new framework for conceptualizing causes based on complex adaptive systems. Thinking of causes as dynamical constraints makes bottom-up and top-down causal relations, including those involving intentional causes, suddenly tractable. A different logic for explaining actions—as historical narrative, not inference—follows if one adopts this novel approach to long-standing questions of action and responsibility.



The Hidden Structure of Interaction

Author : Luigi Anolli

Publisher : IOS Press

Page : 308 pages

File Size : 33,20 MB

Release : 2005

Category : Computers

ISBN : 9781586035099

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Book Description

The idea of complexity states that most things tend to organize themselves into recurring patterns, even when these patterns are not immediately visible to an external observer. The general name for the scientific field concerned with the behaviour over time of a dynamic system is complexity theory. The dynamic systems - systems capable of changing over time - are the focus of this approach, and its concern is with the predictability of their behaviour. The systems of interest to the complexity theory, under certain conditions, perform in regular, predictable ways; under other conditions they exhibit behaviour in which regularity and predictability is lost. The concepts of stable and unstable behaviour are part of the traditional repertoire of physical science. What is novel is the concept of something in between - chaotic behaviour. For chaos here we refer to systems which display behaviour that, though it has certain regularities, defies prediction. How does the order emerge from the chaos? How can we predict the behaviour of a chaotic system?Over the last 30 years and more, trying to identify the hidden patterns behind chaotic behaviour became the focus of attention in a number of scientific disciplines. These range as widely as astronomy, chemistry, evolutionary biology, geology and psychology.