Complex Nonlinearity

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Complex Nonlinearity

Vladimir G. Ivancevic,Tijana T. Ivancevic
Complex Nonlinearity Book PDF

Author : Vladimir G. Ivancevic,Tijana T. Ivancevic
Publisher : Springer Science & Business Media
Page : 855 pages
File Size : 52,9 Mb
Release : 2008-05-31
Category : Science
ISBN : 9783540793571

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Complex Nonlinearity by Vladimir G. Ivancevic,Tijana T. Ivancevic Pdf

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.

Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics

Ramon G. Rubio,Yuri S. Ryazantsev,Victor M Starov,Guo-Xiang Huang,Alexander P Chetverikov,Paolo Arena,Alex A. Nepomnyashchy,Alberto Ferrus,Eugene G. Morozov
Without Bounds A Scientific Canvas of Nonlinearity and Complex Dynamics Book PDF

Author : Ramon G. Rubio,Yuri S. Ryazantsev,Victor M Starov,Guo-Xiang Huang,Alexander P Chetverikov,Paolo Arena,Alex A. Nepomnyashchy,Alberto Ferrus,Eugene G. Morozov
Publisher : Springer
Page : 799 pages
File Size : 42,5 Mb
Release : 2013-05-30
Category : Science
ISBN : 9783642340703

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Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics by Ramon G. Rubio,Yuri S. Ryazantsev,Victor M Starov,Guo-Xiang Huang,Alexander P Chetverikov,Paolo Arena,Alex A. Nepomnyashchy,Alberto Ferrus,Eugene G. Morozov Pdf

Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the research areas covered by the famous Instituto Pluridisciplinar at the Universidad Complutense of Madrid, which he co-founded over two decades ago, and include: fluid physics and related nonlinear phenomena at interfaces and in other geometries, wetting and spreading dynamics, geophysical and astrophysical flows, and novel aspects of electronic transport in anharmonic lattices, as well as topics in neurodynamics and robotics.

Dynamics Of Complex Systems

Yaneer Bar-yam
Dynamics Of Complex Systems Book PDF

Author : Yaneer Bar-yam
Publisher : CRC Press
Page : 866 pages
File Size : 55,5 Mb
Release : 2019-03-04
Category : Mathematics
ISBN : 9780429717598

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Dynamics Of Complex Systems by Yaneer Bar-yam Pdf

This book aims to develop models and modeling techniques that are useful when applied to all complex systems. It adopts both analytic tools and computer simulation. The book is intended for students and researchers with a variety of backgrounds.

Nonlinear and Adaptive Control of Complex Systems

A.L. Fradkov,I.V. Miroshnik,V.O. Nikiforov
Nonlinear and Adaptive Control of Complex Systems Book PDF

Author : A.L. Fradkov,I.V. Miroshnik,V.O. Nikiforov
Publisher : Springer Science & Business Media
Page : 520 pages
File Size : 47,8 Mb
Release : 2013-06-29
Category : Science
ISBN : 9789401592611

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Nonlinear and Adaptive Control of Complex Systems by A.L. Fradkov,I.V. Miroshnik,V.O. Nikiforov Pdf

This volume presents a theoretical framework and control methodology for a class of complex dynamical systems characterised by high state space dimension, multiple inputs and outputs, significant nonlinearity, parametric uncertainty, and unmodeled dynamics. A unique feature of the authors' approach is the combination of rigorous concepts and methods of nonlinear control (invariant and attracting submanifolds, Lyapunov functions, exact linearisation, passification) with approximate decomposition results based on singular perturbations and decentralisation. Some results published previously in the Russian literature and not well known in the West are brought to light. Basic concepts of modern nonlinear control and motivating examples are given. Audience: This book will be useful for researchers, engineers, university lecturers and postgraduate students specialising in the fields of applied mathematics and engineering, such as automatic control, robotics, and control of vibrations.

Complex and Chaotic Nonlinear Dynamics

Thierry Vialar
Complex and Chaotic Nonlinear Dynamics Book PDF

Author : Thierry Vialar
Publisher : Springer Science & Business Media
Page : 752 pages
File Size : 49,7 Mb
Release : 2009-04-26
Category : Business & Economics
ISBN : 9783540859789

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Complex and Chaotic Nonlinear Dynamics by Thierry Vialar Pdf

Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the ambitious goal to bring together an extensive body of knowledge regarding complex dynamics from various academic disciplines. Beyond its focus on economics and finance, including for instance the evolution of macroeconomic growth models towards nonlinear structures as well as signal processing applications to stock markets, fundamental parts of the book are devoted to the use of nonlinear dynamics in mathematics, statistics, signal theory and processing. Numerous examples and applications, almost 700 illustrations and numerical simulations based on the use of Matlab make the book an essential reference for researchers and students from many different disciplines who are interested in the nonlinear field. An appendix recapitulates the basic mathematical concepts required to use the book.

Nonlinear Dynamics in Optical Complex Systems

Kenju Otsuka
Nonlinear Dynamics in Optical Complex Systems Book PDF

Author : Kenju Otsuka
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 49,9 Mb
Release : 2000-04-30
Category : Technology & Engineering
ISBN : 0792361326

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Nonlinear Dynamics in Optical Complex Systems by Kenju Otsuka Pdf

This book is the first comprehensive volume on nonlinear dynamics and chaos in optical systems. A few books have been published recently, but they summarize applied mathematical methodologies toward understanding of nonlinear dynamics in laser systems with small degrees of freedom focusing on linearized perturbation and bifurcation analyses. In contrast to these publications, this book summarizes nonlinear dynamic problems in optical complex systems possessing large degrees of freedom, systematically featuring our original experimental results and their theoretical treatments. The new concepts introduced in this book will have a wide appeal to audiences involved in a rapidly-growing field of nonlinear dynamics. This book focuses on nonlinear dynamics and cooperative functions in realistic optical complex systems, such as multimode lasers, laser array, coupled nonlinear-element systems, and their applications to optical processing. This book is prepared for graduate students majoring in optical and laser physics, but the generic nature of complex systems described in this book may stimulate researchers in the field of nonlinear dynamics covering different academic areas including applied mathematics, hydrodynamics, celestial mechanics, chemistry, biology, and economics.

Nonlinearity, Bounded Rationality, and Heterogeneity

Tamotsu Onozaki
Nonlinearity Bounded Rationality and Heterogeneity Book PDF

Author : Tamotsu Onozaki
Publisher : Springer
Page : 220 pages
File Size : 42,7 Mb
Release : 2018-01-28
Category : Business & Economics
ISBN : 9784431549710

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Nonlinearity, Bounded Rationality, and Heterogeneity by Tamotsu Onozaki Pdf

This book pursues a nonlinear approach in considering both chaotic dynamical models and agent-based simulation models of economics, as well as their dynamical behaviors. Three key concepts arising in this context are “nonlinearity,” “bounded rationality” and “heterogeneity,” which also make up the title of the book. Nonlinearity is the warp that runs throughout all models because systems that exhibit chaotic or other complex behavior in the absence of any exogenous disturbances are absolutely nonlinear. Bounded rationality constitutes the woof, because economic systems do not exhibit complex behavior if all agents are perfectly rational, as is usually assumed in neoclassical economics. Agents who are boundedly rational have to struggle to do their best with limited information and tend to adapt to their economic environment without knowing what is the best. Furthermore, the heterogeneity of firms or consumers dyes the fabric of complex dynamics woven from the warp and woof.

Nonlinear Dynamics in Complex Systems

Armin Fuchs
Nonlinear Dynamics in Complex Systems Book PDF

Author : Armin Fuchs
Publisher : Springer Science & Business Media
Page : 237 pages
File Size : 44,5 Mb
Release : 2012-09-22
Category : Technology & Engineering
ISBN : 9783642335525

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Nonlinear Dynamics in Complex Systems by Armin Fuchs Pdf

With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified. This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh-Rose). Part III may serve as a refresher and companion of some mathematical basics that have been forgotten or were not covered in basic math courses. Finally, the appendix contains an explicit derivation and basic numerical methods together with some programming examples as well as solutions to the exercises provided at the end of certain chapters. Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work. “This book is a masterful treatment, one might even say a gift, to the interdisciplinary scientist of the future.” “With the authoritative voice of a genuine practitioner, Fuchs is a master teacher of how to handle complex dynamical systems.” “What I find beautiful in this book is its clarity, the clear definition of terms, every step explained simply and systematically.” (J.A.Scott Kelso, excerpts from the foreword)

Nonlinear Mechanics of Complex Structures

Holm Altenbach,Marco Amabili,Yuri V. Mikhlin
Nonlinear Mechanics of Complex Structures Book PDF

Author : Holm Altenbach,Marco Amabili,Yuri V. Mikhlin
Publisher : Springer Nature
Page : 476 pages
File Size : 46,6 Mb
Release : 2021-07-29
Category : Science
ISBN : 9783030758905

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Nonlinear Mechanics of Complex Structures by Holm Altenbach,Marco Amabili,Yuri V. Mikhlin Pdf

This book covers different topics of nonlinear mechanics in complex structures, such as the appearance of new nonlinear phenomena and the behavior of finite-dimensional and distributed nonlinear systems, including numerous systems directly connected with important technological problems.

Complex Valued Nonlinear Adaptive Filters

Danilo P. Mandic,Vanessa Su Lee Goh
Complex Valued Nonlinear Adaptive Filters Book PDF

Author : Danilo P. Mandic,Vanessa Su Lee Goh
Publisher : John Wiley & Sons
Page : 344 pages
File Size : 54,5 Mb
Release : 2009-04-20
Category : Science
ISBN : 9780470742631

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Complex Valued Nonlinear Adaptive Filters by Danilo P. Mandic,Vanessa Su Lee Goh Pdf

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 Structural Engineering

Demeter G. Fertis
Nonlinear Structural Engineering Book PDF

Author : Demeter G. Fertis
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 47,6 Mb
Release : 2007-05-05
Category : Technology & Engineering
ISBN : 9783540329763

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Nonlinear Structural Engineering by Demeter G. Fertis Pdf

This book concentrates on the nonlinear static and dynamic analysis of structures and structural components that are widely used in everyday engineering applications. It presents unique methods for nonlinear problems which permits the correct usage of powerful linear methods. Every topic is thoroughly explained and includes numerical examples. The new concepts, theories and methods introduced simplify the solution of the complex nonlinear problems.

Essentials of Nonlinear Circuit Dynamics with MATLAB® and Laboratory Experiments

Arturo Buscarino,Luigi Fortuna,Mattia Frasca
Essentials of Nonlinear Circuit Dynamics with MATLAB and Laboratory Experiments Book PDF

Author : Arturo Buscarino,Luigi Fortuna,Mattia Frasca
Publisher : CRC Press
Page : 261 pages
File Size : 43,7 Mb
Release : 2017-04-07
Category : Technology & Engineering
ISBN : 9781351849722

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Essentials of Nonlinear Circuit Dynamics with MATLAB® and Laboratory Experiments by Arturo Buscarino,Luigi Fortuna,Mattia Frasca Pdf

This book deals with nonlinear dynamics of electronic circuits, which could be used in robot control, secure communications, sensors and synchronized networks. The genesis of the content is related to a course on complex adaptive systems that has been held at the University of Catania since 2005. The efforts are devoted in order to emulate with nonlinear electronic circuits nonlinear dynamics. Step-by-step methods show the essential concepts of complex systems by using the Varela diagrams and accompanying MATLAB® exercises to reinforce new information. Special attention has been devoted to chaotic systems and networks of chaotic circuits by exploring the fundamentals, such as synchronization and control. The aim of the book is to give to readers a comprehensive view of the main concepts of nonlinear dynamics to help them better understand complex systems and their control through the use of electronics devices.

Complex Systems Theory and Development Practice

Samir Rihani
Complex Systems Theory and Development Practice Book PDF

Author : Samir Rihani
Publisher : Zed Books
Page : 308 pages
File Size : 51,5 Mb
Release : 2002
Category : Business & Economics
ISBN : 1842770470

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Complex Systems Theory and Development Practice by Samir Rihani Pdf

"Ranging over a wide terrain of social, political and economic thinking and specific country experiences, the author explains the key concepts in complex systems theory and their possible applications in development practice. He examines various development issues and institutions in the light of what he sees as the limitations of rigid linear thinking in an essentially fluid, non-linear world. Little wonder, he concludes, that the results of half a century of development effort have been so disappointing."--BOOK JACKET.

Nonlinear Dynamics and Chaos

Steven H. Strogatz
Nonlinear Dynamics and Chaos Book PDF

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 55,9 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9780429961113

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Nonlinear Dynamics and Chaos by Steven H. Strogatz Pdf

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Nonlinear Dynamical Economics and Chaotic Motion

Hans-Walter Lorenz
Nonlinear Dynamical Economics and Chaotic Motion Book PDF

Author : Hans-Walter Lorenz
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642783241

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Nonlinear Dynamical Economics and Chaotic Motion by Hans-Walter Lorenz Pdf

Usually, the first edition of a book still contains a multiplicity of typographic, con ceptional, and computational errors even if one believes the opposite at the time of publication. As this book did not represent a counterexample to this rule, the current second edition offers a chance to remove at least the known shortcomings. The book has been partly re-organized. The previously rather long Chapter 4 has been split into two separate chapters dealing with discrete-time and continuous time approaches to nonlinear economic dynamics. The short summary of basic properties of linear dynamical systems has been banned to an appendix because the line of thought in the chapter seems to have been unnecessarily interrupted by these technical details and because the book concentrates on nonlinear systems. This appendix, which mainly deals with special formal properties of dynamical sys tems, also contains some new material on invariant subspaces and center-manifold reductions. A brief introduction into the theory of lags and operators is followed by a few remarks on the relation between the 'true' properties of dynamical systems and their behavior observable in numerical experiments. Additional changes in the main part of the book include a re-consideration of Popper's determinism vs. inde terminism discussion in the light of chaotic properties of deterministic, nonlinear systems in Chapter 1. An investigation of a simultaneous price-quantity adjustment process, a more detailed inquiry into the uniqueness property of limit cycles, and a short presentation of relaxation oscillations are included in Chapter 2.