Emergence Of Dynamical Order
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Emergence Of Dynamical Order
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Author : Susanna C Manrubia
language : en
Publisher: World Scientific
Release Date : 2004-04-14
Emergence Of Dynamical Order written by Susanna C Manrubia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-14 with Science categories.
' 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 '
Emergence Of Dynamical Order
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Author : Susanna C. Manrubia
language : en
Publisher: World Scientific
Release Date : 2004
Emergence Of Dynamical Order written by Susanna C. Manrubia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Large populations of interacting active elements, periodic or chaotic, can undergo spontaneous transitions to dynamically ordered states. These collective states are characterized by self-organized coherence revealed by full mutual synchronization of individual dynamics or the formation of multiple synchronous clusters. Such self-organization phenomena are essential for the functioning of complex systems of various origins, both natural and artificial. This book provides a detailed introduction to the theory of collective synchronization phenomena in large complex systems. Transitions to dynamical clustering and synchronized states are systematically discussed. Such concepts as dynamical order parameters, glass like behavior and hierarchical organization are presented.
Between Chaos And Synchronization
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Author : Santiago Gil
language : de
Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
Release Date : 2011-03
Between Chaos And Synchronization written by Santiago Gil and has been published by Sudwestdeutscher Verlag Fur Hochschulschriften AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03 with categories.
Models of phase oscillators have proven to be a very convenient tool to investigate the emergence of dynamical order in complex systems, and their use has been spreading across disciplines ranging from chemistry to biology, neurology and economics, to name a few. In particular, they have been used as a probing model to study the interplay between network structure and dynamics on networks for systems of broadly different nature. This work concerns itself with the emergence and destruction of dynamical order in networks of phase oscillators. Particular attention is payed to the implementation of methods to control the formation and behavior of self-organized dynamical patterns in the transition landscape between synchronization and chaos. This book consists of a revised version of the author's doctoral thesis, presented at the Technische Universitat Berlin in January 2010, and defended with a magna cum laude distinction."
Order And Chaos In Dynamical Astronomy
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Author : George Contopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Order And Chaos In Dynamical Astronomy written by George Contopoulos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.
This book is one of the first to provide a general overview of order and chaos in dynamical astronomy. The progress of the theory of chaos has a profound impact on galactic dynamics. It has even invaded celestial mechanics, since chaos was found in the solar system which in the past was considered as a prototype of order. The book provides a unifying approach to these topics from an author who has spent more than 50 years of research in the field. The first part treats order and chaos in general. The other two parts deal with order and chaos in galaxies and with other applications in dynamical astronomy, ranging from celestial mechanics to general relativity and cosmology.
In The Wake Of Chaos
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Author : Stephen H. Kellert
language : en
Publisher: University of Chicago Press
Release Date : 1994-10-28
In The Wake Of Chaos written by Stephen H. Kellert and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-28 with Science categories.
Chaos theory has captured scientific and popular attention. What began as the discovery of randomness in simple physical systems has become a widespread fascination with "chaotic" models of everything from business cycles to brainwaves to heart attacks. But what exactly does this explosion of new research into chaotic phenomena mean for our understanding of the world? In this timely book, Stephen Kellert takes the first sustained look at the broad intellectual and philosophical questions raised by recent advances in chaos theory—its implications for science as a source of knowledge and for the very meaning of that knowledge itself.
Quasi Periodic Motions In Families Of Dynamical Systems
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Author : Hendrik W. Broer
language : en
Publisher: Springer
Release Date : 2009-01-25
Quasi Periodic Motions In Families Of Dynamical Systems written by Hendrik W. Broer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-25 with Mathematics categories.
This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for their use in modelling the dynamics related to frictionless mechanics, including the planetary and lunar motions. In this context the general picture appears to be as follows. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confined to invariant tori. On the other hand, systems exist that are entirely chaotic on each energy level. In between we know systems that, being sufficiently small perturbations of integrable ones, exhibit coexistence of order (invariant tori carrying quasi-periodic dynamics) and chaos (the so called stochastic layers). The Kolmogorov-Arnol'd-Moser (KAM) theory on quasi-periodic motions tells us that the occurrence of such motions is open within the class of all Hamiltonian systems: in other words, it is a phenomenon persistent under small Hamiltonian perturbations. Moreover, generally, for any such system the union of quasi-periodic tori in the phase space is a nowhere dense set of positive Lebesgue measure, a so called Cantor family. This fact implies that open classes of Hamiltonian systems exist that are not ergodic. The main aim of the book is to study the changes in this picture when other classes of systems - or contexts - are considered.
Emergence In Complex Cognitive Social And Biological Systems
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Author : Gianfranco Minati
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Emergence In Complex Cognitive Social And Biological Systems written by Gianfranco Minati and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
The systems movement is made up of many systems societies as well as of disciplinary researchers and researches, explicitly or implicitly focusing on the subject of systemics, officially introduced in the scientific community fifty years ago. Many researches in different fields have been and continue to be sources of new ideas and challenges for the systems community. To this regard, a very important topic is the one of EMERGENCE. Between the goals for the actual and future systems scientists there is certainly the definition of a general theory of emergence and the building of a general model of it. The Italian Systems Society, Associazione Italiana per la Ricerca sui Sistemi (AIRS), decided to devote its Second National Conference to this subject. Because AIRS is organized under the form of a network of researchers, institutions, scholars, professionals, and teachers, its research activity has an impact at different levels and in different ways. Thus the topic of emergence was not only the focus of this conference but it is actually the main subject of many AIRS activities.
Chaotic Worlds From Order To Disorder In Gravitational N Body Dynamical Systems
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Author : B.A. Steves
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-22
Chaotic Worlds From Order To Disorder In Gravitational N Body Dynamical Systems written by B.A. Steves and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-22 with Science categories.
Based on the recent NATO Advanced Study Institute "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems", this state of the art textbook, written by internationally renowned experts, provides an invaluable reference volume for all students and researchers in gravitational n-body systems. The contributions are especially designed to give a systematic development from the fundamental mathematics which underpin modern studies of ordered and chaotic behaviour in n-body dynamics to their application to real motion in planetary systems. This volume presents an up-to-date synoptic view of the subject.
Order And Chaos In Dynamical Astronomy
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Author : George Contopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-16
Order And Chaos In Dynamical Astronomy written by George Contopoulos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-16 with Science categories.
This book is one of the first to provide a general overview of order and chaos in dynamical astronomy. The progress of the theory of chaos has a profound impact on galactic dynamics. It has even invaded celestial mechanics, since chaos was found in the solar system which in the past was considered as a prototype of order. The book provides a unifying approach to these topics from an author who has spent more than 50 years of research in the field. The first part treats order and chaos in general. The other two parts deal with order and chaos in galaxies and with other applications in dynamical astronomy, ranging from celestial mechanics to general relativity and cosmology.
Permutation Complexity In Dynamical Systems
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Author : José Amigó
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-20
Permutation Complexity In Dynamical Systems written by José Amigó and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-20 with Science categories.
The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods, while periodicity is not. Another interesting feature is that since it can be shown that random (unconstrained) dynamics has no forbidden patterns with probability one, their existence can be used as a fingerprint to identify any deterministic origin of orbit generation. This book is primarily addressed to researchers working in the field of nonlinear dynamics and complex systems, yet will also be suitable for graduate students interested in these subjects. The presentation is a compromise between mathematical rigor and pedagogical approach. Accordingly, some of the more mathematical background needed for more in depth understanding has been shifted into the appendices.