Nonlinear Dynamics Chaotic And Complex Systems
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Nonlinear Dynamics Chaotic And Complex Systems
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Author : Eryk Infeld
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-19
Nonlinear Dynamics Chaotic And Complex Systems written by Eryk Infeld and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-19 with Mathematics categories.
The physics and mathematics of nonlinear dynamics, chaotic and complex systems constitute some of the most fascinating developments of late twentieth century science. It turns out that chaotic bahaviour can be understood, and even utilized, to a far greater degree than had been suspected. Surprisingly, universal constants have been discovered. The implications have changed our understanding of important phenomena in physics, biology, chemistry, economics, medicine and numerous other fields of human endeavor. In this book, two dozen scientists and mathematicians who were deeply involved in the "nonlinear revolution" cover most of the basic aspects of the field.
Nonlinear Dynamics And Entropy Of Complex Systems With Hidden And Self Excited Attractors
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Author : Christos Volos
language : en
Publisher: MDPI
Release Date : 2019-05-03
Nonlinear Dynamics And Entropy Of Complex Systems With Hidden And Self Excited Attractors written by Christos Volos and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-03 with Technology & Engineering categories.
In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.
Applications Of Nonlinear Dynamics
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Author : Visarath In
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Applications Of Nonlinear Dynamics written by Visarath In 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 2009-02-11 with Technology & Engineering categories.
The ?eld of applied nonlinear dynamics has attracted scientists and engineers across many different disciplines to develop innovative ideas and methods to study c- plex behavior exhibited by relatively simple systems. Examples include: population dynamics, ?uidization processes, applied optics, stochastic resonance, ?ocking and ?ightformations,lasers,andmechanicalandelectricaloscillators. Acommontheme among these and many other examples is the underlying universal laws of nonl- ear science that govern the behavior, in space and time, of a given system. These laws are universal in the sense that they transcend the model-speci?c features of a system and so they can be readily applied to explain and predict the behavior of a wide ranging phenomena, natural and arti?cial ones. Thus the emphasis in the past decades has been in explaining nonlinear phenomena with signi?cantly less att- tion paid to exploiting the rich behavior of nonlinear systems to design and fabricate new devices that can operate more ef?ciently. Recently, there has been a series of meetings on topics such as Experimental Chaos, Neural Coding, and Stochastic Resonance, which have brought together many researchers in the ?eld of nonlinear dynamics to discuss, mainly, theoretical ideas that may have the potential for further implementation. In contrast, the goal of the 2007 ICAND (International Conference on Applied Nonlinear Dynamics) was focused more sharply on the implementation of theoretical ideas into actual - vices and systems.
Complex Nonlinearity
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Author : Vladimir G. Ivancevic
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-31
Complex Nonlinearity written by Vladimir G. Ivancevic 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 2008-05-31 with Science categories.
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.
Nonlinear Dynamics Chaos And Complexity
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Author : Dimitri Volchenkov
language : en
Publisher: Springer Nature
Release Date : 2020-12-14
Nonlinear Dynamics Chaos And Complexity written by Dimitri Volchenkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-14 with Mathematics categories.
This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe a complex nexus of dependences in multi-level complex systems and to effectively engineer their important functions. The collection of works devoted to the memory of Professor Valentin Afraimovich introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in physics, machine learning, brain and urban dynamics. The book can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, urban planners, and even musicians (with some mathematical background).
Foundations Of Complex Systems
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Author : Gregoire Nicolis
language : en
Publisher: World Scientific
Release Date : 2007
Foundations Of Complex Systems written by Gregoire Nicolis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.
A geometric process is a simple monotone process that was first introduced by the author in 1988. It is a generalization of renewal process. This book captures the extensive research work on geometric processes that has been done since then in both probability and statistics theory and various applications. Some results are published for the first time. A reference book for researchers and a handbook for practioners, it is also a useful textbook for postgraduate or senior undergraduate students.
Nonlinear Dynamics And Chaos Advances And Perspectives
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Author : Marco Thiel
language : en
Publisher: Springer
Release Date : 2010-05-17
Nonlinear Dynamics And Chaos Advances And Perspectives written by Marco Thiel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-17 with Science categories.
This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.
Chaos
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Author : Angelo Vulpiani
language : en
Publisher: World Scientific
Release Date : 2010
Chaos written by Angelo Vulpiani 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 Mathematics categories.
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.
Instabilities Chaos And Turbulence
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Author : Paul Manneville
language : en
Publisher: World Scientific
Release Date : 2010
Instabilities Chaos And Turbulence written by Paul Manneville 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.
This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.
Applications Of Chaos And Nonlinear Dynamics In Science And Engineering Vol 3
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Author : Santo Banerjee
language : en
Publisher: Springer
Release Date : 2013-06-12
Applications Of Chaos And Nonlinear Dynamics In Science And Engineering Vol 3 written by Santo Banerjee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-12 with Science categories.
Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This third volume concentrates on reviewing further relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such fluctuation relations and chaotic dynamics in physics, fractals and their applications in epileptic seizures, as well as chaos synchronization. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications.