Nonlinear Dynamics In Complex Systems

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Nonlinear Dynamics in Complex Systems

Author : Armin Fuchs
Publisher : Springer Science & Business Media
ISBN 13 : 3642335527
Total Pages : 237 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Nonlinear Dynamics in Complex Systems by : Armin Fuchs

Download or read book Nonlinear Dynamics in Complex Systems written by Armin Fuchs and published by Springer Science & Business Media. This book was released on 2012-09-22 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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)

Dynamics Of Complex Systems

Author : Yaneer Bar-yam
Publisher : CRC Press
ISBN 13 : 0429717598
Total Pages : 866 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Dynamics Of Complex Systems by : Yaneer Bar-yam

Download or read book Dynamics Of Complex Systems written by Yaneer Bar-yam and published by CRC Press. This book was released on 2019-03-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Complex Dynamics

Author : José António Tenreiro Machado
Publisher : Springer Science & Business Media
ISBN 13 : 9781461402312
Total Pages : 332 pages
Book Rating : 4.4/5 (23 download)

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Book Synopsis Nonlinear and Complex Dynamics by : José António Tenreiro Machado

Download or read book Nonlinear and Complex Dynamics written by José António Tenreiro Machado and published by Springer Science & Business Media. This book was released on 2011-08-28 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and earth-to-halo transfers in the sun, earth and moon. Part II presents the dynamics of complex systems including bio-systems, neural systems, chemical systems and hydro-dynamical systems. Finally, Part III covers economic and financial systems including market uncertainty, inflation, economic activity and foreign competition and the role of nonlinear dynamics in each.

Nonlinear Dynamics, Chaos, and Complexity

Author : Dimitri Volchenkov
Publisher : Springer Nature
ISBN 13 : 9811590346
Total Pages : 198 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Nonlinear Dynamics, Chaos, and Complexity by : Dimitri Volchenkov

Download or read book Nonlinear Dynamics, Chaos, and Complexity written by Dimitri Volchenkov and published by Springer Nature. This book was released on 2020-12-14 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Applications of Nonlinear Dynamics

Author : Visarath In
Publisher : Springer Science & Business Media
ISBN 13 : 3540856323
Total Pages : 464 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Applications of Nonlinear Dynamics by : Visarath In

Download or read book Applications of Nonlinear Dynamics written by Visarath In and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of Complex Systems

Author : G. Nicolis
Publisher : World Scientific
ISBN 13 : 9812700439
Total Pages : 343 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Foundations of Complex Systems by : G. Nicolis

Download or read book Foundations of Complex Systems written by G. Nicolis and published by World Scientific. This book was released on 2007 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from nonlinear science, statistical physics and numerical simulation. It is shown how these developments lead to an understanding, both qualitative and quantitative, of the complex systems encountered in nature and in everyday experience and, conversely, how natural complexity acts as a source of inspiration for progress at the fundamental level.

Foundations of Complex Systems

Author : Gregoire Nicolis
Publisher : World Scientific
ISBN 13 : 981277565X
Total Pages : 343 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Foundations of Complex Systems by : Gregoire Nicolis

Download or read book Foundations of Complex Systems written by Gregoire Nicolis and published by World Scientific. This book was released on 2007 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems

Author : M. Reza Rahimi Tabar
Publisher : Springer
ISBN 13 : 3030184722
Total Pages : 280 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems by : M. Reza Rahimi Tabar

Download or read book Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems written by M. Reza Rahimi Tabar and published by Springer. This book was released on 2019-07-04 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.

Nonlinear Dynamics and Chaos

Author : Steven H. Strogatz
Publisher : CRC Press
ISBN 13 : 0429961111
Total Pages : 532 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz

Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Dynamics

Author : George Datseris
Publisher : Springer Nature
ISBN 13 : 3030910326
Total Pages : 243 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Nonlinear Dynamics by : George Datseris

Download or read book Nonlinear Dynamics written by George Datseris and published by Springer Nature. This book was released on 2022-03-13 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at students and researchers in all the diverse fields in which nonlinear phenomena are important. Since most tasks in nonlinear dynamics cannot be treated analytically, skills in using numerical simulations are crucial for analyzing these phenomena. The text therefore addresses in detail appropriate computational methods as well as identifying the pitfalls of numerical simulations. It includes numerous executable code snippets referring to open source Julia software packages. Each chapter includes a selection of exercises with which students can test and deepen their skills.

Philosophy of Complex Systems

Author :
Publisher : Elsevier
ISBN 13 : 9780080931227
Total Pages : 952 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Philosophy of Complex Systems by :

Download or read book Philosophy of Complex Systems written by and published by Elsevier. This book was released on 2011-05-23 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt: The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on. Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years. -Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included

Complex Nonlinearity

Author : Vladimir G. Ivancevic
Publisher : Springer Science & Business Media
ISBN 13 : 3540793577
Total Pages : 855 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Complex Nonlinearity by : Vladimir G. Ivancevic

Download or read book Complex Nonlinearity written by Vladimir G. Ivancevic and published by Springer Science & Business Media. This book was released on 2008-05-31 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Entropy of Complex Systems with Hidden and Self-excited Attractors

Author : Christos Volos
Publisher : MDPI
ISBN 13 : 3038978981
Total Pages : 290 pages
Book Rating : 4.0/5 (389 download)

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Book Synopsis Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors by : Christos Volos

Download or read book Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors written by Christos Volos and published by MDPI. This book was released on 2019-05-03 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Complex Systems and Networks

Author : Jinhu Lü
Publisher : Springer
ISBN 13 : 3662478242
Total Pages : 482 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Complex Systems and Networks by : Jinhu Lü

Download or read book Complex Systems and Networks written by Jinhu Lü and published by Springer. This book was released on 2015-08-14 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elementary book provides some state-of-the-art research results on broad disciplinary sciences on complex networks. It presents an in-depth study with detailed description of dynamics, controls and applications of complex networks. The contents of this book can be summarized as follows. First, the dynamics of complex networks, for example, the cluster dynamic analysis by using kernel spectral methods, community detection algorithms in bipartite networks, epidemiological modeling with demographics and epidemic spreading on multi-layer networks, are studied. Second, the controls of complex networks are investigated including topics like distributed finite-time cooperative control of multi-agent systems by applying homogenous-degree and Lyapunov methods, composite finite-time containment control for disturbed second-order multi-agent systems, fractional-order observer design of multi-agent systems, chaos control and anticontrol of complex systems via Parrondos game and many more. Third, the applications of complex networks provide some applicable carriers, which show the importance of theories developed in complex networks. In particular, a general model for studying time evolution of transition networks, deflection routing in complex networks, recommender systems for social networks analysis and mining, strategy selection in networked evolutionary games, integration and methods in computational biology, are discussed in detail.

Synchronization in Complex Networks of Nonlinear Dynamical Systems

Author : Chai Wah Wu
Publisher : World Scientific
ISBN 13 : 9812709746
Total Pages : 168 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Synchronization in Complex Networks of Nonlinear Dynamical Systems by : Chai Wah Wu

Download or read book Synchronization in Complex Networks of Nonlinear Dynamical Systems written by Chai Wah Wu and published by World Scientific. This book was released on 2007 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ideas from systems theory, linear algebra and graph theory and the synergy between them that are necessary to derive synchronization conditions. Many of the results, which have been obtained fairly recently and have until now not appeared in textbook form, are presented with complete proofs. This text is suitable for graduate-level study or for researchers who would like to be better acquainted with the latest research in this area. Sample Chapter(s). Chapter 1: Introduction (76 KB). Contents: Graphs, Networks, Laplacian Matrices and Algebraic Connectivity; Graph Models; Synchronization in Networks of Nonlinear Continuous-Time Dynamical Systems; Synchronization in Networks of Coupled Discrete-Time Systems; Synchronization in Network of Systems with Linear Dynamics; Agreement and Consensus Problems in Groups of Interacting Agents. Readership: Graduate students and researchers in physics, applied mathematics and engineering.

Nonlinear Dynamics

Author : Muthusamy Lakshmanan
Publisher : Springer Science & Business Media
ISBN 13 : 3642556884
Total Pages : 628 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Nonlinear Dynamics by : Muthusamy Lakshmanan

Download or read book Nonlinear Dynamics written by Muthusamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

The Dynamics of Complex Urban Systems

Author : Sergio Albeverio
Publisher : Springer Science & Business Media
ISBN 13 : 3790819379
Total Pages : 484 pages
Book Rating : 4.7/5 (98 download)

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Book Synopsis The Dynamics of Complex Urban Systems by : Sergio Albeverio

Download or read book The Dynamics of Complex Urban Systems written by Sergio Albeverio and published by Springer Science & Business Media. This book was released on 2007-10-16 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the contributions presented at the international workshop "The Dynamics of Complex Urban Systems: an interdisciplinary approach" held in Ascona, Switzerland in November 2004. Experts from several disciplines outline a conceptual framework for modeling and forecasting the dynamics of both growth-limited cities and megacities. Coverage reflects the various interdependencies between structural and social development.