Dynamics Of Complex Systems

This book aims to develop models and modeling techniques that are useful when applied to all complex systems.

Dynamics Of Complex Systems

Author: Yaneer Bar-yam

Publisher: CRC Press

ISBN: 0429697589

Page: 864

View: 733

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 Dynamics in Complex Systems

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 ...

Nonlinear Dynamics in Complex Systems

Author: Armin Fuchs

Publisher: Springer Science & Business Media

ISBN: 3642335527

Page: 238

View: 475

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)

Model Emergent Dynamics in Complex Systems

Chapter 19 Coordinate transforms separate slow from fast in nonautonomous
dynamics Contents 19.1 Model an example nonlinear nonautonomous system . .
. . 586 19.1.1 Simplifyingfastdynamicsinvolvesmemory . . . . 587 19.1.2 Split
forcing ...

Model Emergent Dynamics in Complex Systems

Author: A. J. Roberts

Publisher: SIAM

ISBN: 1611973562

Page: 750

View: 417

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.

Stochastic Dynamics of Complex Systems

Complex Dynamics: Tools and Applications: Characterization of Collective Dynamics; Markovian Stochastic Processes; Monte Carlo Methods; Record Statistics and Extremal Statistics; Complexity and Hierarchies; Energy Landscapes; Record ...

Stochastic Dynamics of Complex Systems

Author: Paolo Sibani

Publisher:

ISBN: 9781848169937

Page: 281

View: 664

Complex Dynamics: Tools and Applications: Characterization of Collective Dynamics; Markovian Stochastic Processes; Monte Carlo Methods; Record Statistics and Extremal Statistics; Complexity and Hierarchies; Energy Landscapes; Record Dynamics and Marginal Stability; Complex Systems with Similar Dynamics: Ageing of Spin Glasses; Magnetic Relaxation in Superconductors; Ageing of Colloids; Evolving Biological Systems; Non-stationary Ageing Dynamics in Ant Societies; Epilogue: What is Complexity Science?

Dynamics of Complex Quantum Systems

This book gathers together a range of similar problems that can be encountered in different fields of modern quantum physics and that have common features with regard to multilevel quantum systems.

Dynamics of Complex Quantum Systems

Author: Vladimir M. Akulin

Publisher: Springer Science & Business Media

ISBN: 940077205X

Page: 677

View: 112

This book gathers together a range of similar problems that can be encountered in different fields of modern quantum physics and that have common features with regard to multilevel quantum systems. The main motivation was to examine from a uniform standpoint various models and approaches that have been developed in atomic, molecular, condensed matter, chemical, laser and nuclear physics in various contexts. The book should help senior-level undergraduate, graduate students and researchers putting particular problems in these fields into a broader scientific context and thereby taking advantage of well-established techniques used in adjacent fields. This second edition has been expanded to include substantial new material (e.g. new sections on Dynamic Localization and on Euclidean Random Matrices and new chapters on Entanglement, Open Quantum Systems, and Coherence Protection). It is based on the author’s lectures at the Moscow Institute of Physics and Technology, at the CNRS Aimé Cotton Laboratory, and on other courses he has given over the last two decades.

Geometrical Dynamics of Complex Systems

1 Introduction As stated in the preface , the objective of this monograph is a
unified rigorous geometrical dynamics of complex systems of various natures ,
where by ' complex systems ' we mean high - dimensional nonlinear systems (
with or ...

Geometrical Dynamics of Complex Systems

Author: Vladimir G. Ivancevic

Publisher: Taylor & Francis

ISBN: 9781402045448

Page: 822

View: 599

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.

The Synchronized Dynamics of Complex Systems

The Synchronized Dynamics of Complex Systems STEFANO BOCCALETTI CNR
– Istituto dei Sistemi Complessi Florence, Italy and Embassy of Italy in Tel Aviv
Tel Aviv, Israel AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW ...

The Synchronized Dynamics of Complex Systems

Author: Stefano Boccaletti

Publisher: Elsevier

ISBN: 9780080560427

Page: 258

View: 497

The origin of the word synchronization is a greek root, meaning "to share the common time". The original meaning of synchronization has been maintained up to now in the colloquial use of this word, as agreement or correlation in time of different processes. Historically, the analysis of synchronization phenomena in the evolution of dynamical systems has been a subject of active investigation since the earlier days of physics. Recently, the search for synchronization has moved to chaotic systems. In this latter framework, the appearance of collective (synchronized) dynamics is, in general, not trivial. Indeed, a dynamical system is called chaotic whenever its evolution sensitively depends on the initial conditions. The above said implies that two trajectories emerging from two different closeby initial conditions separate exponentially in the course of the time. As a result, chaotic systems intrinsically defy synchronization, because even two identical systems starting from slightly different initial conditions would evolve in time in a unsynchronized manner (the differences in the systems' states would grow exponentially). This is a relevant practical problem, insofar as experimental initial conditions are never known perfectly. The setting of some collective (synchronized) behavior in coupled chaotic systems has therefore a great importance and interest. The subject of the present book is to summarize the recent discoveries involving the study of synchronization in coupled chaotic systems. Not always the word synchronization is taken as having the same colloquial meaning, and one needs to specify what synchrony means in all particular contexts in which we will describe its emergence. The book describes the complete synchronization phenomenon, both for low and for high dimensional situations, and illustrates possible applications in the field of communicating with chaos. Furthermore, the book summarizes the concepts of phase synchronization, lag synchronization, imperfect phase synchronization, and generalized synchronization, describing a general transition scenario between a hierarchy of different types of synchronization for chaotic oscillators. These concepts are extended to the case of structurally different systems, of uncoupled systems subjected to a common external source, of space extended nonlinearly evolving fields, and of dynamical units networking via a complex wiring of connections, giving thus a summary of all possible situations that are encountered in real life and in technology. · Technical, but not specialistic language · About 100 illustrative Figures · Full overview on synchronization phenomena · Review of the main tools and techniques used in the field · Paradigmatic examples and experiments illustrating the basic concepts · Full Reference to the main publications existing in the literature on the subject

The Dynamics of Complex Urban Systems

Claes Andersson Department of Physical Resource Theory, Chalmers University
of Technology, Götheborg, Sweden Abstract In this paper the ontogeny of
complex systems models is discussed: the historical aspect of model ontology.

The Dynamics of Complex Urban Systems

Author: Sergio Albeverio

Publisher: Springer Science & Business Media

ISBN: 3790819379

Page: 484

View: 879

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.

Modeling Complex Systems

This book illustrates how models of complex systems are built up and provides indispensable mathematical tools for studying their dynamics.

Modeling Complex Systems

Author: Nino Boccara

Publisher: Springer Science & Business Media

ISBN: 9781441965622

Page: 490

View: 608

This book illustrates how models of complex systems are built up and provides indispensable mathematical tools for studying their dynamics. This second edition includes more recent research results and many new and improved worked out examples and exercises.

Dynamics of Complex Interconnected Systems Networks and Bioprocesses

Introduction Networks is tool to describe systems composed of many different
units which each typically interact with a few of the other units. Networks thus
used to quantify complex systems from the intricate interactions of proteins inside
a ...

Dynamics of Complex Interconnected Systems  Networks and Bioprocesses

Author: Arne T. Skjeltorp

Publisher: Springer Science & Business Media

ISBN: 1402050305

Page: 209

View: 557

This book reviews the synergism between various fields of research that are confronted with networks, such as genetic and metabolic networks, social networks, the Internet and ecological systems. In many cases, the interacting networks manifest so-called emergent properties that are not possessed by any of the individual components. Knowledge gained from the study of complex non-biological systems can be applied to the intricate braided relationships that govern cellular functions.

Coherent Dynamics of Complex Quantum Systems

One may say that the majority of problems of contemporary interest are of this
type. Statistics is a natural way to describe large systems. Initially, the statistical
approach to individual complex quantum objects had been formulated in the
context ...

Coherent Dynamics of Complex Quantum Systems

Author: Vladimir M. Akulin

Publisher: Springer Science & Business Media

ISBN: 3540210520

Page: 472

View: 970

Coherent Dynamics of Complex Quantum Systems is aimed at senior-level undergraduate students in the areas of atomic, molecular, and laser physics, physical chemistry, quantum optics and quantum informatics. It should help them put particular problems in these fields into a broader scientific context and thereby take advantage of the well-elaborated technique of the adjacent fields.

Complex Dynamics

Readers learn to predict and control low- and high-dimensional as well as continuous- and discrete-time nonlinear systems dynamics in complex variables.

Complex Dynamics

Author: Vladimir G. Ivancevic

Publisher: Springer

ISBN: 9789048176311

Page: 810

View: 923

Readers learn to predict and control low- and high-dimensional as well as continuous- and discrete-time nonlinear systems dynamics in complex variables. In the final chapter, all the previously developed methods are used to present the "Holy Grail" of modern physical and cosmological science, the search for the "theory of everything" and the "true" cosmological dynamics.

Quantum Dynamics of Complex Molecular Systems

Decoherence in Combined Quantum Mechanical and Classical Mechanical
Methods for Dynamics as Illustrated for ... a recurring theme in the treatment of
complex systems because a full quantum mechanical treatment is usually
possible only ...

Quantum Dynamics of Complex Molecular Systems

Author: David A. Micha

Publisher: Springer Science & Business Media

ISBN: 3540344608

Page: 429

View: 931

Quantum phenomena are ubiquitous in complex molecular systems - as revealed by many experimental observations based upon ultrafast spectroscopic techniques - and yet remain a challenge for theoretical analysis. The present volume, based on a May 2005 workshop, examines and reviews the state-of-the-art in the development of new theoretical and computational methods to interpret the observed phenomena. Emphasis is on complex molecular processes involving surfaces, clusters, solute-solvent systems, materials, and biological systems. The research summarized in this book shows that much can be done to explain phenomena in systems excited by light or through atomic interactions. It demonstrates how to tackle the multidimensional dynamics arising from the atomic structure of a complex system, and addresses phenomena in condensed phases as well as phenomena at surfaces. The chapters on new methodological developments cover both phenomena in isolated systems, and phenomena which involve the statistical effects of an environment, such as fluctuations and dissipation. The methodology part explores new rigorous ways to formulate mixed quantum-classical dynamics in many dimensions, along with new ways to solve a many-atom Schroedinger equation, or the Liouville-von Neumann equation for the density operator, using trajectories and ideas related to hydrodynamics. Part I treats applications to complex molecular systems, and Part II covers new theoretical and computational methods

A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems

This book collects recent developments in nonlinear and complex systems.

A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems

Author: Elbert E. N. Macau

Publisher: Springer

ISBN: 3319785125

Page: 228

View: 985

This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry groups, conservation laws, risk reduction management, barriers in Hamiltonian systems, and synchronization and chaotic transient. Illustrating mathematical modeling applications to nonlinear physics and nonlinear engineering, the book is ideal for academic and industrial researchers concerned with machinery and controls, manufacturing, and controls. · Introduces new concepts for understanding and modeling complex systems; · Explains risk reduction management in complex systems; · Examines the symmetry group approach to understanding complex systems; · Illustrates the relation between transient chaos and crises.

Complex Human Dynamics

This book, edited and authored by a closely collaborating network of social scientists and psychologists, recasts typical research topics in these fields into the language of nonlinear, dynamic and complex systems.

Complex Human Dynamics

Author: Andrzej Nowak

Publisher: Springer

ISBN: 3642314368

Page: 242

View: 144

This book, edited and authored by a closely collaborating network of social scientists and psychologists, recasts typical research topics in these fields into the language of nonlinear, dynamic and complex systems. The aim is to provide scientists with different backgrounds - physics, applied mathematics and computer sciences - with the opportunity to apply the tools of their trade to an altogether new range of possible applications. At the same time, this book will serve as a first reference for a new generation of social scientists and psychologists wishing to familiarize themselves with the new methodology and the "thinking in complexity".

Slow Dynamics in Complex Systems

3rd International Symposium on Slow Dynamics in Complex Systems American
Institute of Physics Michio Tokuyama, Irwin Oppenheim. The Principle for Artificial
Molecular Machine and Noise : Slow Stochastic Dynamics in Complex Systems ...

Slow Dynamics in Complex Systems

Author: American Institute of Physics

Publisher: American Institute of Physics

ISBN:

Page: 829

View: 905

This book gives up-to-date information on the liquid-glass transition in various disciplines, such as physics, chemistry, biology, engineering, polymer science, and computer science. The book contains review articles by leading scientists and contributed papers by authors in the forefront of research. The systems studied covered almost all states of matter including solids, liquids, complex solutions, polymers, and suspensions. Significant progress was made on a variety of topics. Among these were experimental and theoretical studies of colloidal systems; experiments on glass to glass transitions in micellar systems; theoretical studies of polyelectrolytes and polymer melts and networks; theoretical and computer studies of hydrodynamics in suspensions and Rayleigh-Taylor and Rayleigh-Couette instabilities; theoretical and experimental studies of the glass transition; computer simulations of the glass transition in thin films; vibrational motions in glass forming liquids and glasses; the effects of shear on supercooled liquids; engineering and experimental studies of metallic glasses; mode-coupling studies of complex glass formation; and Lorentz gas studies of the translational and rotational motion of a rigid rod.

The Evolutionary Dynamics of Complex Systems

Their reproductive life is complex , but that is another matter ( or another mater ) .
NET generates models of evolutionary processes which contain both “ initial
conditions ” and “ boundary conditions ” components . Systems with one sort of ...

The Evolutionary Dynamics of Complex Systems

Author: Charles Dyke

Publisher: Oxford University Press on Demand

ISBN:

Page: 161

View: 912

The book seeks unities among things often thought to be different from one another; but it also insists on the differences among things often squashed into unities.

Instabilities Chaos and Turbulence

This book is an introduction to the application of nonlinear dynamics to problems of stability, chaos and turbulence arising in continuous media and their connection to dynamical systems.

Instabilities  Chaos and Turbulence

Author: Paul Manneville

Publisher: Imperial College Press

ISBN: 9781860944918

Page: 391

View: 884

This book is an introduction to the application of nonlinear dynamics to problems of stability, chaos and turbulence arising in continuous media and their connection to dynamical systems. With an emphasis on the understanding of basic concepts, it should be of interest to nearly any science-oriented undergraduate and potentially to anyone who wants to learn about recent advances in the field of applied nonlinear dynamics. Technicalities are, however, not completely avoided. They are instead explained as simply as possible using heuristic arguments and specific worked examples.

Dynamics of Complex Autonomous Boolean Networks

Complex. Systems. In a network description, multi-agent systems, such as
collections of interacting genes, assemblies of interconnected neurons, or social
communities, are approximated as sets of nodes and edges. Nodes interact with
each ...

Dynamics of Complex Autonomous Boolean Networks

Author: David P. Rosin

Publisher: Springer

ISBN: 3319135783

Page: 199

View: 479

This thesis focuses on the dynamics of autonomous Boolean networks, on the basis of Boolean logic functions in continuous time without external clocking. These networks are realized with integrated circuits on an electronic chip as a field programmable gate array (FPGA) with roughly 100,000 logic gates, offering an extremely flexible model system. It allows fast and cheap design cycles and large networks with arbitrary topologies and coupling delays. The author presents pioneering results on theoretical modeling, experimental realization, and selected applications. In this regard, three classes of novel dynamic behavior are investigated: (i) Chaotic Boolean networks are proposed as high-speed physical random number generators with high bit rates. (ii) Networks of periodic Boolean oscillators are home to long-living transient chimera states, i.e., novel patterns of coexisting domains of spatially coherent (synchronized) and incoherent (desynchronized) dynamics. (iii) Excitable networks exhibit cluster synchronization and can be used as fast artificial Boolean neurons whose spiking patterns can be controlled. This work presents the first experimental platform for large complex networks, which will facilitate exciting future developments.