Complex Nonlinearity
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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.
Complex Valued Nonlinear Adaptive Filters
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Author : Danilo P. Mandic
language : en
Publisher: John Wiley & Sons
Release Date : 2009-04-20
Complex Valued Nonlinear Adaptive Filters written by Danilo P. Mandic and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Science categories.
This book was written in response to the growing demand for a text that provides a unified treatment of linear and nonlinear complex valued adaptive filters, and methods for the processing of general complex signals (circular and noncircular). It brings together adaptive filtering algorithms for feedforward (transversal) and feedback architectures and the recent developments in the statistics of complex variable, under the powerful frameworks of CR (Wirtinger) calculus and augmented complex statistics. This offers a number of theoretical performance gains, which is illustrated on both stochastic gradient algorithms, such as the augmented complex least mean square (ACLMS), and those based on Kalman filters. This work is supported by a number of simulations using synthetic and real world data, including the noncircular and intermittent radar and wind signals.
Nonlinear Structures And Systems Volume 1
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Author : Gaetan Kerschen
language : en
Publisher: Springer
Release Date : 2019-06-28
Nonlinear Structures And Systems Volume 1 written by Gaetan Kerschen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-28 with Science categories.
Nonlinear Structures & Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, the first volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear Reduced-order Modeling Jointed Structures: Identification, Mechanics, Dynamics Experimental Nonlinear Dynamics Nonlinear Model & Modal Interactions Nonlinear Damping Nonlinear Modeling & Simulation Nonlinearity & System Identification
Recent Trends In Chaotic Nonlinear And Complex Dynamics
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Author : Jan Awrejcewicz
language : en
Publisher: World Scientific
Release Date : 2021-07-26
Recent Trends In Chaotic Nonlinear And Complex Dynamics written by Jan Awrejcewicz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-26 with Science categories.
In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.
Nonlinear Universe Unveiling Complexity In Nature And Beyond
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-15
Nonlinear Universe Unveiling Complexity In Nature And Beyond written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-15 with Science categories.
In "Nonlinear Universe: Unveiling Complexity in Nature and Beyond," readers are taken on a captivating journey through the realm of nonlinear phenomena, exploring their profound implications across diverse fields of science and beyond. This book offers a comprehensive and accessible introduction to the intricate world of nonlinearity, providing a fresh perspective on familiar concepts and opening up new avenues for exploration and understanding. Nonlinearity, the departure from linearity in the relationship between input and output, gives rise to a mesmerizing array of complex and intriguing behaviors, including chaos, fractals, and self-organization. Nonlinear systems exhibit a remarkable sensitivity to initial conditions, often leading to unpredictable and counterintuitive outcomes. This book delves into these concepts, explaining them in a clear and engaging manner, making them accessible to readers from all backgrounds. Through a blend of theoretical explanations, real-world examples, and captivating illustrations, "Nonlinear Universe" illuminates the intricate workings of nonlinearity in various scientific disciplines. From the chaotic dynamics of weather patterns to the intricate interactions of social networks, this book showcases the ubiquity and diversity of nonlinear phenomena. With its comprehensive coverage, engaging writing style, and thought-provoking insights, "Nonlinear Universe" is an invaluable resource for students, researchers, and anyone fascinated by the complexities of nature. It is an invitation to explore the frontiers of science and discover the hidden connections that shape our world. This book offers a unique perspective on nonlinearity, highlighting its profound implications for our understanding of the universe. It provides a deeper appreciation for the intricate beauty and complexity of the world around us, revealing the underlying patterns and connections that govern its behavior. "Nonlinear Universe" is a must-read for anyone seeking to expand their knowledge of nonlinear science and its far-reaching applications. It is a captivating exploration of the nonlinear universe, unlocking its mysteries and inspiring readers to see the world in a new light. If you like this book, write a review!
Nonlinearity Bifurcation And Chaos
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Author : Jan Awrejcewicz
language : en
Publisher: BoD – Books on Demand
Release Date : 2012-10-24
Nonlinearity Bifurcation And Chaos written by Jan Awrejcewicz and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-24 with Mathematics categories.
Nonlinearity, Bifurcation and Chaos - Theory and Application is an edited book focused on introducing both theoretical and application oriented approaches in science and engineering. It contains 12 chapters, and is recommended for university teachers, scientists, researchers, engineers, as well as graduate and post-graduate students either working or interested in the field of nonlinearity, bifurcation and chaos.
Strong Nonlinear Oscillators
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Author : Livija Cveticanin
language : en
Publisher: Springer
Release Date : 2017-05-29
Strong Nonlinear Oscillators written by Livija Cveticanin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-29 with Technology & Engineering categories.
This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author’s original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear oscillators is enlarged and a variety of procedures for solving free strong nonlinear oscillators is suggested. A method for error estimation is also given which is suitable to compare the exact and approximate solutions. Besides the oscillators with one degree-of-freedom, the one and two mass oscillatory systems with two-degrees-of-freedom and continuous oscillators are considered. The chaos and chaos suppression in ideal and non-ideal mechanical systems is explained. In this second edition more attention is given to the application of the suggested methodologies and obtained results to some practical problems in physics, mechanics, electronics and biomechanics. Thus, for the oscillator with two degrees-of-freedom, a generalization of the solving procedure is performed. Based on the obtained results, vibrations of the vocal cord are analyzed. In the book the vibration of the axially purely nonlinear rod as a continuous system is investigated. The developed solving procedure and the solutions are applied to discuss the muscle vibration. Vibrations of an optomechanical system are analyzed using the oscillations of an oscillator with odd or even quadratic nonlinearities. The extension of the forced vibrations of the system is realized by introducing the Ateb periodic excitation force which is the series of a trigonometric function. The book is self-consistent and suitable for researchers and as a textbook for students and also professionals and engineers who apply these techniques to the field of nonlinear oscillations.
Control Of Self Organizing Nonlinear Systems
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Author : Eckehard Schöll
language : en
Publisher: Springer
Release Date : 2016-01-22
Control Of Self Organizing Nonlinear Systems written by Eckehard Schöll and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-22 with Science categories.
The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.
Stochasticity Nonlinearity And Forecasting Of Streamflow Processes
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Author : Wen Wang
language : en
Publisher: IOS Press
Release Date : 2006
Stochasticity Nonlinearity And Forecasting Of Streamflow Processes written by Wen Wang and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Computers categories.
Streamflow forecasting is of great importance to water resources management and flood defense. On the other hand, a better understanding of the streamflow process is fundamental for improving the skill of streamflow forecasting. The methods for forecasting streamflows may fall into two general classes: process-driven methods and data-driven methods. Equivalently, methods for understanding streamflow processes may also be broken into two categories: physically-based methods and mathematically-based methods. This thesis focuses on using mathematically-based methods to analyze stochasticity and nonlinearity of streamflow processes based on univariate historic streamflow records, and presents data-driven models that are also mainly based on univariate streamflow time series. Six streamflow processes of five rivers in different geological regions are investigated for stochasticity and nonlinearity at several characteristic timescales.
Nonparametric Identification Of Nonlinear Dynamic Systems
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Author : Kenderi, Gábor
language : en
Publisher: KIT Scientific Publishing
Release Date : 2018-11-11
Nonparametric Identification Of Nonlinear Dynamic Systems written by Kenderi, Gábor and has been published by KIT Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-11 with Identification categories.
A nonparametric identification method for highly nonlinear systems is presented that is able to reconstruct the underlying nonlinearities without a priori knowledge of the describing nonlinear functions. The approach is based on nonlinear Kalman Filter algorithms using the well-known state augmentation technique that turns the filter into a dual state and parameter estimator, of which an extension towards nonparametric identification is proposed in the present work.