Stochastic Dynamics Of Complex Systems

Author : Paolo Sibani,Henrik Jeldtoft Jensen
Publisher : World Scientific Publishing Company
Page : 300 pages
File Size : 46,5 Mb
Release : 2013-02-20
Category : Mathematics
ISBN : 9781848169951

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Stochastic Dynamics of Complex Systems by Paolo Sibani,Henrik Jeldtoft Jensen Pdf

Dynamical evolution over long time scales is a prominent feature of all the systems we intuitively think of as complex — for example, ecosystems, the brain or the economy. In physics, the term ageing is used for this type of slow change, occurring over time scales much longer than the patience, or indeed the lifetime, of the observer. The main focus of this book is on the stochastic processes which cause ageing, and the surprising fact that the ageing dynamics of systems which are very different at the microscopic level can be treated in similar ways. The first part of this book provides the necessary mathematical and computational tools and the second part describes the intuition needed to deal with these systems. Some of the first few chapters have been covered in several other books, but the emphasis and selection of the topics reflect both the authors' interests and the overall theme of the book. The second part contains an introduction to the scientific literature and deals in some detail with the description of complex phenomena of a physical and biological nature, for example, disordered magnetic materials, superconductors and glasses, models of co-evolution in ecosystems and even of ant behaviour. These heterogeneous topics are all dealt with in detail using similar analytical techniques. This book emphasizes the unity of complex dynamics and provides the tools needed to treat a large number of complex systems of current interest. The ideas and the approach to complex dynamics it presents have not appeared in book form until now.

Author : Henrik Jeldtoft Jensen,Paolo Sibani
Publisher : Unknown
Page : 300 pages
File Size : 48,9 Mb
Release : 2013
Category : Electronic books
ISBN : 1848169949

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Stochastic Dynamics of Complex Systems by Henrik Jeldtoft Jensen,Paolo Sibani Pdf

Author : Yaneer Bar-yam
Publisher : CRC Press
Page : 864 pages
File Size : 44,8 Mb
Release : 2019-03-04
Category : Mathematics
ISBN : 9780429697586

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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.

Author : Anonim
Publisher : Unknown
Page : 340 pages
File Size : 41,9 Mb
Release : 2005
Category : Noise
ISBN : UOM:39015058302459

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Noise in Complex Systems and Stochastic Dynamics by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,7 Mb
Release : 2024-06-10
Category : Electronic
ISBN : 9789814476942

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Foundations of Complex Systems by Anonim Pdf

Author : Visarath In,Patrick Longhini,Antonio Palacios
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 50,7 Mb
Release : 2009-02-11
Category : Technology & Engineering
ISBN : 9783540856320

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Applications of Nonlinear Dynamics by Visarath In,Patrick Longhini,Antonio Palacios Pdf

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 : A. J. Roberts
Publisher : SIAM
Page : 760 pages
File Size : 46,6 Mb
Release : 2014-12-18
Category : Mathematics
ISBN : 9781611973556

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Model Emergent Dynamics in Complex Systems by A. J. Roberts Pdf

Arising out of the growing interest in and applications of modern dynamical systems theory, this book explores how to derive relatively simple dynamical equations that model complex physical interactions. The author’s objectives are to use sound theory to explore algebraic techniques, develop interesting applications, and discover general modeling principles. Model Emergent Dynamics in Complex Systems unifies into one powerful and coherent approach the many varied extant methods for mathematical model reduction and approximation. Using mathematical models at various levels of resolution and complexity, the book establishes the relationships between such multiscale models and clarifying difficulties and apparent paradoxes and addresses model reduction for systems, resolves initial conditions, and illuminates control and uncertainty. The basis for the author’s methodology is the theory and the geometric picture of both coordinate transforms and invariant manifolds in dynamical systems; in particular, center and slow manifolds are heavily used. The wonderful aspect of this approach is the range of geometric interpretations of the modeling process that it produces—simple geometric pictures inspire sound methods of analysis and construction. Further, pictures drawn of state spaces also provide a route to better assess a model’s limitations and strengths. Geometry and algebra form a powerful partnership and coordinate transforms and manifolds provide a powerfully enhanced and unified view of a swathe of other complex system modeling methodologies such as averaging, homogenization, multiple scales, singular perturbations, two timing, and WKB theory. Audience Advanced undergraduate and graduate students, engineers, scientists, and other researchers who need to understand systems and modeling at different levels of resolution and complexity will all find this book useful.

Author : Andreas Schadschneider,Debashish Chowdhury,Katsuhiro Nishinari
Publisher : Elsevier
Page : 582 pages
File Size : 55,8 Mb
Release : 2010-10-01
Category : Science
ISBN : 0080560520

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Stochastic Transport in Complex Systems by Andreas Schadschneider,Debashish Chowdhury,Katsuhiro Nishinari Pdf

The first part of the book provides a pedagogical introduction to the physics of complex systems driven far from equilibrium. In this part we discuss the basic concepts and theoretical techniques which are commonly used to study classical stochastic transport in systems of interacting driven particles. The analytical techniques include mean-field theories, matrix product ansatz, renormalization group, etc. and the numerical methods are mostly based on computer simulations. In the second part of the book these concepts and techniques are applied not only to vehicular traffic but also to transport and traffic-like phenomena in living systems ranging from collective movements of social insects (for example, ants) on trails to intracellular molecular motor transport. These demonstrate the conceptual unity of the fundamental principles underlying the apparent diversity of the systems and the utility of the theoretical toolbox of non-equilibrium statistical mechanics in interdisciplinary research far beyond the traditional disciplinary boundaries of physics. Leading industry experts provide a broad overview of the interdisciplinary nature of physics Presents unified descriptions of intracellular, ant, and vehicular traffic from a physics point of view Applies theoretical methods in practical everyday situations Reference and guide for physicists, engineers and graduate students

Author : E. Goles,Servet Martínez
Publisher : Springer Science & Business Media
Page : 185 pages
File Size : 53,8 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401713238

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Dynamics of Complex Interacting Systems by E. Goles,Servet Martínez Pdf

This book contains the courses given at the Fourth School on Statistical Physics and Cooperative Systems held at Santiago, Chile, from 12th to 16th December 1994. This School brings together scientists working on subjects related to recent trends in complex systems. Some of these subjects deal with dynamical systems, ergodic theory, cellular automata, symbolic and arithmetic dynamics, spatial systems, large deviation theory and neural networks. Scientists working in these subjects come from several aeras: pure and applied mathematics, non linear physics, biology, computer science, electrical engineering and artificial intelligence. Each contribution is devoted to one or more of the previous subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The expository text of Roberto Livi concerns the study of coupled map lattices (CML) as models of spatially extended dynamical systems. CML is one of the most used tools for the investigation of spatially extended systems. The paper emphasizes rigorous results about the dynamical behavior of one dimensional CML; i.e. a uniform real local function defined in the interval [0,1], interacting with its nearest neighbors in a one dimensional lattice.

Author : Vladimir G. Ivancevic,Tijana T. Ivancevic
Publisher : Taylor & Francis
Page : 856 pages
File Size : 51,7 Mb
Release : 2006-01-18
Category : Language Arts & Disciplines
ISBN : 1402045441

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Geometrical Dynamics of Complex Systems by Vladimir G. Ivancevic,Tijana T. Ivancevic Pdf

Geometrical Dynamics of Complex Systems is a graduate-level monographic textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical dynamicsofcomplexsystemsofvariousnatures. By'complexsystems', inthis book are meant high-dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a uni?ed geometrical - proachtodynamicsofcomplexsystemsofvariouskinds: engineering, physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these multi-input multi-output (MIMO) systems have something in common: the underlying physics. However, instead of dealing with the pop- 1 ular 'soft complexity philosophy', we rather propose a rigorous geometrical and topological approach. We believe that our rigorous approach has much greater predictive power than the soft one. We argue that science and te- nology is all about prediction and control. Observation, understanding and explanation are important in education at undergraduate level, but after that it should be all prediction and control. The main objective of this book is to show that high-dimensional nonlinear systems and processes of 'real life' can be modelled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. It is well-known that linear systems, which are completely predictable and controllable by de?nition - live only in Euclidean spaces (of various - mensions). They are as simple as possible, mathematically elegant and fully elaborated from either scienti?c or engineering side. However, in nature, no- ing is linear. In reality, everything has a certain degree of nonlinearity, which means: unpredictability, with subsequent uncontrollability.

Author : A. J. Roberts
Publisher : SIAM
Page : 750 pages
File Size : 49,8 Mb
Release : 2024-06-10
Category : Mathematics
ISBN : 9781611973563

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Model Emergent Dynamics in Complex Systems by A. J. Roberts Pdf

Arising out of the growing interest in and applications of modern dynamical systems theory, this book explores how to derive relatively simple dynamical equations that model complex physical interactions. The author?s objectives are to use sound theory to explore algebraic techniques, develop interesting applications, and discover general modeling principles. Model Emergent Dynamics in Complex Systems unifies into one powerful and coherent approach the many varied extant methods for mathematical model reduction and approximation. Using mathematical models at various levels of resolution and complexity, the book establishes the relationships between such multiscale models and clarifying difficulties and apparent paradoxes and addresses model reduction for systems, resolves initial conditions, and illuminates control and uncertainty. The basis for the author?s methodology is the theory and the geometric picture of both coordinate transforms and invariant manifolds in dynamical systems; in particular, center and slow manifolds are heavily used. The wonderful aspect of this approach is the range of geometric interpretations of the modeling process that it produces?simple geometric pictures inspire sound methods of analysis and construction. Further, pictures drawn of state spaces also provide a route to better assess a model?s limitations and strengths. Geometry and algebra form a powerful partnership and coordinate transforms and manifolds provide a powerfully enhanced and unified view of a swathe of other complex system modeling methodologies such as averaging, homogenization, multiple scales, singular perturbations, two timing, and WKB theory.

Author : G. Nicolis,Cathy Nicolis
Publisher : World Scientific
Page : 343 pages
File Size : 48,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812700438

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Foundations of Complex Systems by G. Nicolis,Cathy Nicolis Pdf

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 : Eryk Infeld,R. Zelazny,A. Galkowski
Publisher : Cambridge University Press
Page : 358 pages
File Size : 51,9 Mb
Release : 1997-06-19
Category : Mathematics
ISBN : 0521582016

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Nonlinear Dynamics, Chaotic and Complex Systems by Eryk Infeld,R. Zelazny,A. Galkowski Pdf

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.

Author : Kunihiko Kaneko,Ichiro Tsuda
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 51,7 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9783642568619

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Complex Systems: Chaos and Beyond by Kunihiko Kaneko,Ichiro Tsuda Pdf

This book, the first in a series on this subject, is the outcome of many years of efforts to give a new all-encompassing approach to complex systems in nature based on chaos theory. While maintaining a high level of rigor, the authors avoid an overly complicated mathematical apparatus, making the book accessible to a wider interdisciplinary readership.

Author : Armin Fuchs
Publisher : Springer Science & Business Media
Page : 237 pages
File Size : 55,7 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)