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Author: Armin Fuchs Publisher: Springer Science & Business Media ISBN: 3642335527 Category : Technology & Engineering Languages : en Pages : 237
Book Description
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)
Author: Armin Fuchs Publisher: Springer Science & Business Media ISBN: 3642335527 Category : Technology & Engineering Languages : en Pages : 237
Book Description
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)
Author: Yaneer Bar-yam Publisher: CRC Press ISBN: 0429717598 Category : Mathematics Languages : en Pages : 866
Book Description
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.
Author: G. Nicolis Publisher: World Scientific ISBN: 9812700439 Category : Mathematics Languages : en Pages : 343
Book Description
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.
Author: Dimitri Volchenkov Publisher: Springer Nature ISBN: 9811590346 Category : Mathematics Languages : en Pages : 198
Book Description
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).
Author: Visarath In Publisher: Springer Science & Business Media ISBN: 3540856323 Category : Technology & Engineering Languages : en Pages : 464
Book Description
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.
Author: Vladimir G. Ivancevic Publisher: Springer Science & Business Media ISBN: 3540793577 Category : Science Languages : en Pages : 855
Book Description
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.
Author: Kenju Otsuka Publisher: Springer Science & Business Media ISBN: 9780792361329 Category : Technology & Engineering Languages : en Pages : 326
Book Description
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.
Author: José António Tenreiro Machado Publisher: Springer Science & Business Media ISBN: 146140231X Category : Technology & Engineering Languages : en Pages : 328
Book Description
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.
Author: M. Reza Rahimi Tabar Publisher: Springer ISBN: 3030184722 Category : Science Languages : en Pages : 290
Book Description
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.
Author: Chai Wah Wu Publisher: World Scientific ISBN: 9812709746 Category : Mathematics Languages : en Pages : 168
Book Description
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.
Author: Armin Fuchs
Author: Armin Fuchs
Author: Yaneer Bar-yam
Author: G. Nicolis
Author: Dimitri Volchenkov
Author: Visarath In
Author: Vladimir G. Ivancevic
Author: Kenju Otsuka
Author: José António Tenreiro Machado
Author: M. Reza Rahimi Tabar
Author: Chai Wah Wu