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: 146

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: 374

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)

Geometrical Dynamics of Complex Systems

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 ...

Geometrical Dynamics of Complex Systems

Author: Vladimir G. Ivancevic

Publisher: Springer Science & Business Media

ISBN: 140204545X

Page: 824

View: 151

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.

Stochastic Dynamics of Complex Systems

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 ...

Stochastic Dynamics of Complex Systems

Author: Paolo Sibani

Publisher: World Scientific Publishing Company

ISBN: 1848169957

Page: 300

View: 730

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.

The Dynamics of Complex Urban Systems

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.

The Dynamics of Complex Urban Systems

Author: Sergio Albeverio

Publisher: Springer Science & Business Media

ISBN: 3790819379

Page: 484

View: 512

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.

The Evolutionary Dynamics of Complex Systems

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.

The Evolutionary Dynamics of Complex Systems

Author: Charles Dyke

Publisher: Oxford University Press on Demand

ISBN:

Page: 161

View: 490

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.

Model Emergent Dynamics in Complex Systems

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.

Model Emergent Dynamics in Complex Systems

Author: A. J. Roberts

Publisher: SIAM

ISBN: 1611973554

Page: 748

View: 134

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.÷

Slow Dynamics in Complex Systems

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.

Slow Dynamics in Complex Systems

Author: American Institute of Physics

Publisher: American Institute of Physics

ISBN:

Page: 829

View: 377

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.

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: 842

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.

The Synchronized Dynamics of Complex Systems

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 Synchronized Dynamics of Complex Systems

Author: Stefano Boccaletti

Publisher: Elsevier

ISBN: 9780080560427

Page: 258

View: 730

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

Fault Diagnosis of Hybrid Dynamic and Complex Systems

This book presents recent and advanced approaches and techniques that address the complex problem of fault diagnosis of hybrid dynamic and complex systems using different model-based and data-driven approaches in different application ...

Fault Diagnosis of Hybrid Dynamic and Complex Systems

Author: Moamar Sayed-Mouchaweh

Publisher: Springer

ISBN: 3319740148

Page: 286

View: 724

Online fault diagnosis is crucial to ensure safe operation of complex dynamic systems in spite of faults affecting the system behaviors. Consequences of the occurrence of faults can be severe and result in human casualties, environmentally harmful emissions, high repair costs, and economical losses caused by unexpected stops in production lines. The majority of real systems are hybrid dynamic systems (HDS). In HDS, the dynamical behaviors evolve continuously with time according to the discrete mode (configuration) in which the system is. Consequently, fault diagnosis approaches must take into account both discrete and continuous dynamics as well as the interactions between them in order to perform correct fault diagnosis. This book presents recent and advanced approaches and techniques that address the complex problem of fault diagnosis of hybrid dynamic and complex systems using different model-based and data-driven approaches in different application domains (inductor motors, chemical process formed by tanks, reactors and valves, ignition engine, sewer networks, mobile robots, planetary rover prototype etc.). These approaches cover the different aspects of performing single/multiple online/offline parametric/discrete abrupt/tear and wear fault diagnosis in incremental/non-incremental manner, using different modeling tools (hybrid automata, hybrid Petri nets, hybrid bond graphs, extended Kalman filter etc.) for different classes of hybrid dynamic and complex systems.

Complex Systems and Networks

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.

Complex Systems and Networks

Author: Jinhu Lü

Publisher: Springer

ISBN: 3662478242

Page: 482

View: 332

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.

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: 825

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.

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: 617

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.

Coherent Dynamics of Complex Quantum Systems

The purpose of this book is to provide a systematic treatment of these questions and to present a number of exactly solvable problems.

Coherent Dynamics of Complex Quantum Systems

Author: Vladimir M. Akulin

Publisher: Springer Science & Business Media

ISBN: 3540210520

Page: 472

View: 363

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: 302

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.