The Synchronized Dynamics of Complex Systems Book

The Synchronized Dynamics of Complex Systems


  • Author : Stefano Boccaletti
  • Publisher : Elsevier
  • Release Date : 2008-02-05
  • Genre: Science
  • Pages : 258
  • ISBN 10 : 0080560423

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The Synchronized Dynamics of Complex Systems Book Description :

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, imp

Emergence of Dynamical Order Book

Emergence of Dynamical Order


  • Author : Susanna C Manrubia
  • Publisher : World Scientific
  • Release Date : 2004-04-14
  • Genre: Science
  • Pages : 360
  • ISBN 10 : 9789814482950

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Emergence of Dynamical Order Book Description :

' Synchronization processes bring about dynamical order and lead to spontaneous development of structural organization in complex systems of various origins, from chemical oscillators and biological cells to human societies and the brain. This book provides a review and a detailed theoretical analysis of synchronization phenomena in complex systems with different architectures, composed of elements with periodic or chaotic individual dynamics. Special attention is paid to statistical concepts, such as nonequilibrium phase transitions, order parameters and dynamical glasses. Contents:Synchronization and Clustering of Periodic Oscillators:Ensembles of Identical Phase OscillatorsHeterogeneous Ensembles and the Effects of NoiseOscillator NetworksArrays of Limit-Cycle OscillatorsSynchronization and Clustering in Chaotic Systems:Chaos and SynchronizationSynchronization in Populations of Chaotic ElementsClusteringDynamical GlassesSelected Applications:Chemical SystemsBiological CellsNeural Networks Readership: Graduate students and academics interested in complex systems. Keywords:Self-Organization;Nonlinear Dynamics;Chaos;Collective Synchronization;Dynamical Clustering;Hierarchical OrderReviews:“This book makes an additional contribution to the topic paying special attention to statistical concepts, such as nonequilibrium phase transitions, order parameters and dynamical glasses. Another distinguishing feature of the book is that it includes applications in chemistry, cell biology, and brain science.”Zentralblatt MATH '

Complex Systems and Networks Book

Complex Systems and Networks


  • Author : Jinhu Lü
  • Publisher : Springer
  • Release Date : 2015-08-14
  • Genre: Technology & Engineering
  • Pages : 482
  • ISBN 10 : 9783662478240

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Complex Systems and Networks Book Description :

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.

Geometrical Dynamics of Complex Systems Book

Geometrical Dynamics of Complex Systems


  • Author : Vladimir G. Ivancevic
  • Publisher : Taylor & Francis
  • Release Date : 2006-01-18
  • Genre: Language Arts & Disciplines
  • Pages : 822
  • ISBN 10 : 1402045441

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Geometrical Dynamics of Complex Systems Book Description :

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.

A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems Book

A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems


  • Author : Elbert E. N. Macau
  • Publisher : Springer
  • Release Date : 2018-06-14
  • Genre: Technology & Engineering
  • Pages : 228
  • ISBN 10 : 9783319785127

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A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems Book Description :

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.

Synchronization in Complex Networks of Nonlinear Dynamical Systems Book

Synchronization in Complex Networks of Nonlinear Dynamical Systems


  • Author : Chai Wah Wu
  • Publisher : World Scientific
  • Release Date : 2007
  • Genre: Mathematics
  • Pages : 168
  • ISBN 10 : 9789812709745

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Synchronization in Complex Networks of Nonlinear Dynamical Systems 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.

Stochastic Dynamics of Complex Systems Book

Stochastic Dynamics of Complex Systems


  • Author : Paolo Sibani
  • Publisher : World Scientific Publishing Company
  • Release Date : 2013-02-20
  • Genre: Mathematics
  • Pages : 300
  • ISBN 10 : 9781848169951

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Stochastic Dynamics of Complex Systems Book Description :

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.

Consensus and Synchronization in Complex Networks Book

Consensus and Synchronization in Complex Networks


  • Author : Ljupco Kocarev
  • Publisher : Springer
  • Release Date : 2013-01-18
  • Genre: Science
  • Pages : 275
  • ISBN 10 : 9783642333590

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Consensus and Synchronization in Complex Networks Book Description :

In this book for the first time two scientific fields - consensus formation and synchronization of communications - are presented together and examined through their interrelational aspects, of rapidly growing importance. Both fields have indeed attracted enormous research interest especially in relation to complex networks. In networks of dynamic systems (or agents), consensus means to reach an agreement regarding a certain quantity of interest that depends on the state of all dynamical systems (agents). Consensus problems have a long history in control theory and computer sciences, and form the foundation of the field of distributed computing. Synchronization, which defines correlated-in-time behavior between different processes and roots going back to Huygens to the least, is now a highly popular, exciting and rapidly developing topic, with applications ranging from biological networks to mathematical epidemiology, and from processing information in the brain to engineering of communications devices. The book reviews recent finding in both fields and describes novel approaches to consensus formation, where consensus is realized as an instance of the nonlinear dynamics paradigm of chaos synchronization. The chapters are written by world-known experts in both fields and cover topics ranging from fundaments to various applications of consensus and synchronization.

Synchronization Book

Synchronization


  • Author : Stefano Boccaletti
  • Publisher : Cambridge University Press
  • Release Date : 2018-03-29
  • Genre: Mathematics
  • Pages : 255
  • ISBN 10 : 9781107056268

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Synchronization Book Description :

A modern introduction to synchronization phenomena, combining the development of deep mathematical concepts with illustrative examples and practical applications.

Modelling  Estimation and Control of Networked Complex Systems Book

Modelling Estimation and Control of Networked Complex Systems


  • Author : Alessandro Chiuso
  • Publisher : Springer
  • Release Date : 2009-10-13
  • Genre: Technology & Engineering
  • Pages : 238
  • ISBN 10 : 9783642031991

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Modelling Estimation and Control of Networked Complex Systems Book Description :

The paradigm of complexity is pervading both science and engineering, le- ing to the emergence of novel approaches oriented at the development of a systemic view of the phenomena under study; the de?nition of powerful tools for modelling, estimation, and control; and the cross-fertilization of di?erent disciplines and approaches. One of the most promising paradigms to cope with complexity is that of networked systems. Complex, dynamical networks are powerful tools to model, estimate, and control many interesting phenomena, like agent coordination, synch- nization, social and economics events, networks of critical infrastructures, resourcesallocation,informationprocessing,controlovercommunicationn- works, etc. Advances in this ?eld are highlighting approaches that are more and more oftenbasedondynamicalandtime-varyingnetworks,i.e.networksconsisting of dynamical nodes with links that can change over time. Moreover, recent technological advances in wireless communication and decreasing cost and size of electronic devices are promoting the appearance of large inexpensive interconnected systems, each with computational, sensing and mobile ca- bilities. This is fostering the development of many engineering applications, which exploit the availability of these systems of systems to monitor and control very large-scale phenomena with ?ne resolution.

Chaos and Complex Systems Book
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Chaos and Complex Systems


  • Author : Stavros G. Stavrinides
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-19
  • Genre: Science
  • Pages : 581
  • ISBN 10 : 9783642339141

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Chaos and Complex Systems Book Description :

Complexity Science and Chaos Theory are fascinating areas of scientific research with wide-ranging applications. The interdisciplinary nature and ubiquity of complexity and chaos are features that provides scientists with a motivation to pursue general theoretical tools and frameworks. Complex systems give rise to emergent behaviors, which in turn produce novel and interesting phenomena in science, engineering, as well as in the socio-economic sciences. The aim of all Symposia on Chaos and Complex Systems (CCS) is to bring together scientists, engineers, economists and social scientists, and to discuss the latest insights and results obtained in the area of corresponding nonlinear-system complex (chaotic) behavior. Especially for the “4th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems,” which took place April 29th to May 2nd, 2012 in Antalya, Turkey, the scope of the symposium had been further enlarged so as to encompass the presentation of work from circuits to econophysics, and from nonlinear analysis to the history of chaos theory. The corresponding proceedings collected in this volume address a broad spectrum of contemporary topics, including but not limited to networks, circuits, systems, biology, evolution and ecology, nonlinear dynamics and pattern formation, as well as neural, psychological, psycho-social, socio-economic, management complexity and global systems.

Nonlinear and Adaptive Control of Complex Systems Book

Nonlinear and Adaptive Control of Complex Systems


  • Author : A.L. Fradkov
  • Publisher : Springer Science & Business Media
  • Release Date : 1999-07-31
  • Genre: Science
  • Pages : 510
  • ISBN 10 : 0792358929

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Nonlinear and Adaptive Control of Complex Systems Book Description :

This volume presents a theoretical framework and control methodology for a class of complex dynamical systems characterised by high state space dimension, multiple inputs and outputs, significant nonlinearity, parametric uncertainty, and unmodeled dynamics. A unique feature of the authors' approach is the combination of rigorous concepts and methods of nonlinear control (invariant and attracting submanifolds, Lyapunov functions, exact linearisation, passification) with approximate decomposition results based on singular perturbations and decentralisation. Some results published previously in the Russian literature and not well known in the West are brought to light. Basic concepts of modern nonlinear control and motivating examples are given. Audience: This book will be useful for researchers, engineers, university lecturers and postgraduate students specialising in the fields of applied mathematics and engineering, such as automatic control, robotics, and control of vibrations.

Chaotic  Fractional  and Complex Dynamics  New Insights and Perspectives Book

Chaotic Fractional and Complex Dynamics New Insights and Perspectives


  • Author : Mark Edelman
  • Publisher : Springer
  • Release Date : 2017-11-17
  • Genre: Science
  • Pages : 315
  • ISBN 10 : 9783319681092

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Chaotic Fractional and Complex Dynamics New Insights and Perspectives Book Description :

The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic, and fractional dynamics, as well as complex systems and networks – offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to, aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering. As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.

Complex Systems Book

Complex Systems


  • Author : Georgi M. Dimirovski
  • Publisher : Springer
  • Release Date : 2016-05-19
  • Genre: Technology & Engineering
  • Pages : 652
  • ISBN 10 : 9783319288604

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Complex Systems Book Description :

This book gives a wide-ranging description of the many facets of complex dynamic networks and systems within an infrastructure provided by integrated control and supervision: envisioning, design, experimental exploration, and implementation. The theoretical contributions and the case studies presented can reach control goals beyond those of stabilization and output regulation or even of adaptive control. Reporting on work of the Control of Complex Systems (COSY) research program, Complex Systems follows from and expands upon an earlier collection: Control of Complex Systems by introducing novel theoretical techniques for hard-to-control networks and systems. The major common feature of all the superficially diverse contributions encompassed by this book is that of spotting and exploiting possible areas of mutual reinforcement between control, computing and communications. These help readers to achieve not only robust stable plant system operation but also properties such as collective adaptivity, integrity and survivability at the same time retaining desired performance quality. Applications in the individual chapters are drawn from: • the general implementation of model-based diagnosis and systems engineering in medical technology, in communication, and in power and airport networks; • the creation of biologically inspired control brains and safety-critical human–machine systems, • process-industrial uses; • biped robots; • large space structures and unmanned aerial vehicles; and • precision servomechanisms and other advanced technologies. Complex Systems provides researchers from engineering, applied mathematics and computer science backgrounds with innovative theoretical and practical insights into the state-of-the-art of complex networks and systems research. It employs physical implementations and extensive computer simulations. Graduate students specializing in complex-systems research will also learn much from this collection./pp

Complex Systems  Chaos and Beyond Book
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Complex Systems Chaos and Beyond


  • Author : Kunihiko Kaneko
  • Publisher : Springer Science & Business Media
  • Release Date : 2001
  • Genre: Mathematics
  • Pages : 273
  • ISBN 10 : 3540672028

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Complex Systems Chaos and Beyond Book Description :

Chaos in science has always been a fascinating realm since it challenges the usual scientific approach of reductionism. While carefully distinguishing between complexity, holism, randomness, incompleteness, nondeterminism and stochastic behaviour the authors show that, although many aspects of chaos have been phenomenologically understood, most of its defining principles are still difficult to grasp and formulate. Demonstrating that chaos escapes all traditional methods of description, the authors set out to find new methods to deal with this phenomenon and illustrate their constructive approach with many examples from physics, biology and information technology. While maintaining a high level of rigour, an overly complicated mathematical apparatus is avoided in order to make this book accessible, beyond the specialist level, to a wider interdisciplinary readership.

Delay Coupled Complex Systems Book

Delay Coupled Complex Systems


  • Author : Valentin Flunkert
  • Publisher : Springer Science & Business Media
  • Release Date : 2011-06-25
  • Genre: Science
  • Pages : 180
  • ISBN 10 : 3642202500

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Delay Coupled Complex Systems Book Description :

This work addresses time-delay in complex nonlinear systems and, in particular, its applications in complex networks; its role in control theory and nonlinear optics are also investigated. Delays arise naturally in networks of coupled systems due to finite signal propagation speeds and are thus a key issue in many areas of physics, biology, medicine, and technology. Synchronization phenomena in these networks play an important role, e.g., in the context of learning, cognitive and pathological states in the brain, for secure communication with chaotic lasers or for gene regulation. The thesis includes both novel results on the control of complex dynamics by time-delayed feedback and fundamental new insights into the interplay of delay and synchronization. One of the most interesting results here is a solution to the problem of complete synchronization in general networks with large coupling delay, i.e., large distances between the nodes, by giving a universal classification of networks that has a wide range of interdisciplinary applications.

Hypernetworks in the Science of Complex Systems Book

Hypernetworks in the Science of Complex Systems


  • Author : Jeffrey Johnson
  • Publisher : World Scientific
  • Release Date : 2013-11-29
  • Genre: Science
  • Pages : 348
  • ISBN 10 : 9781783264438

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Hypernetworks in the Science of Complex Systems Book Description :

The modern world is complex beyond human understanding and control. The science of complex systems aims to find new ways of thinking about the many interconnected networks of interaction that defy traditional approaches. Thus far, research into networks has largely been restricted to pairwise relationships represented by links between two nodes. This volume marks a major extension of networks to multidimensional hypernetworks for modeling multi-element relationships, such as companies making up the stock market, the neighborhoods forming a city, people making up committees, divisions making up companies, computers making up the internet, men and machines making up armies, or robots working as teams. This volume makes an important contribution to the science of complex systems by: (i) extending network theory to include dynamic relationships between many elements; (ii) providing a mathematical theory able to integrate multilevel dynamics in a coherent way; (iii) providing a new methodological approach to analyze complex systems; and (iv) illustrating the theory with practical examples in the design, management and control of complex systems taken from many areas of application. Contents:IntroductionSets and RelationsHypergraphs and the Galois LatticeSimplicial Complexes and Q-AnalysisBackcloth and Traffic: Dynamics Constrained by TopologyHypernetworksMultilevel SystemsTime, Events, Prediction and ForecastingHypernetworks and DesignPolicy, Design, Planning and ScienceNotes and Reflections Readership: Academics: researchers, scientists, social scientists, complex systems scientists, economists, biologists; Industry: managers, planners, consultants, knowledge professionals, systems engineers, automation specialists, supply chain managers; Public services: Council Officers, city planners, transport planners, health professionals, welfare professionals. Key Features:A first book of its kind on 'hypernetworks', a term the author has coined to describe the mathematical stru

COMPLEX SYSTEM WITH FLOWS AND SYNCHRONIZATION Book

COMPLEX SYSTEM WITH FLOWS AND SYNCHRONIZATION


  • Author : LINFAN MAO
  • Publisher : Infinite Study
  • Release Date :
  • Genre: Mathematics
  • Pages : 24
  • ISBN 10 :

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COMPLEX SYSTEM WITH FLOWS AND SYNCHRONIZATION Book Description :

The main purpose of this lecture is to clarify the complex system with that of contradictory system and its importance to the reality of a thing T by extending Banach or Hilbert spaces to Banach or Hilbert continuity flow spaces over topological graphs and establishing the global differential theory on complex flows.

Complex Systems Book

Complex Systems


  • Author : E. Goles
  • Publisher : Springer Science & Business Media
  • Release Date : 2001-02-28
  • Genre: Mathematics
  • Pages : 301
  • ISBN 10 : 0792368304

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Complex Systems Book Description :

This volume contains the courses given at the Sixth Summer School on Complex Systems held at Facultad de Ciencias Fisicas y Maternaticas, Universidad de Chile at Santiago, Chile, from 14th to 18th December 1998. This school was addressed to graduate students and researchers working on areas related with recent trends in Complex Systems, including dynamical systems, cellular automata, complexity and cutoff in Markov chains. Each contribution is devoted to one of these subjects. In some cases they are structured as surveys, presenting at the same time an original point of view and showing mostly new results. The paper of Pierre Arnoux investigates the relation between low complex systems and chaotic systems, showing that they can be put into relation by some re normalization operations. The case of quasi-crystals is fully studied, in particular the Sturmian quasi-crystals. The paper of Franco Bagnoli and Raul Rechtman establishes relations be tween Lyapunov exponents and synchronization processes in cellular automata. The principal goal is to associate tools, usually used in physical problems, to an important problem in cellularautomata and computer science, the synchronization problem. The paper of Jacques Demongeot and colleagues gives a presentation of at tractors of dynamical systems appearing in biological situations. For instance, the relation between positive or negative loops and regulation systems.

Complex Human Dynamics Book

Complex Human Dynamics


  • Author : Andrzej Nowak
  • Publisher : Springer
  • Release Date : 2013-01-08
  • Genre: Social Science
  • Pages : 242
  • ISBN 10 : 9783642314360

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Complex Human Dynamics Book Description :

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".