Delay-Coupled Complex Systems
Delay-Coupled Complex Systems

Author: Valentin Flunkert

Publisher: Springer Science & Business Media

Published: 2011-06-25

Total Pages: 181

ISBN-13: 3642202500

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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.

Complex Time-Delay Systems
Complex Time-Delay Systems

Author: Fatihcan M. Atay

Publisher: Springer

Published: 2010-03-10

Total Pages: 336

ISBN-13: 3642023290

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One of the major contemporary challenges in both physical and social sciences is modeling, analyzing, and understanding the self-organization, evolution, behavior, and eventual decay of complex dynamical systems ranging from cell assemblies to the human brain to animal societies. The multi-faceted problems in this domain require a wide range of methods from various scienti?c disciplines. There is no question that the inclusion of time delays in complex system models considerably enriches the challenges presented by the problems. Although this inclusion often becomes inevitable as real-world applications demand more and more realistic m- els, the role of time delays in the context of complex systems so far has not attracted the interest it deserves. The present volume is an attempt toward ?lling this gap. There exist various useful tools for the study of complex time-delay systems. At the forefront is the mathematical theory of delay equations, a relatively mature ?eld in many aspects, which provides some powerful techniques for analytical inquiries, along with some other tools from statistical physics, graph theory, computer science, dynamical systems theory, probability theory, simulation and optimization software, and so on. Nevertheless, the use of these methods requires a certain synergy to address complex systems problems, especially in the presence of time delays.

Synchronization in Complex Networks of Nonlinear Dynamical Systems
Synchronization in Complex Networks of Nonlinear Dynamical Systems

Author: Chai Wah Wu

Publisher: World Scientific

Published: 2007

Total Pages: 168

ISBN-13: 9812709746

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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.

Dynamics of Nonlinear Time-Delay Systems
Dynamics of Nonlinear Time-Delay Systems

Author: Muthusamy Lakshmanan

Publisher: Springer Science & Business Media

Published: 2011-01-04

Total Pages: 322

ISBN-13: 3642149383

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Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different branches of science and technology as well as to the synchronization of their coupled versions. Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics and the detailed presentation of real-world applications.

Advances In Analysis And Control Of Time-delayed Dynamical Systems
Advances In Analysis And Control Of Time-delayed Dynamical Systems

Author: Jian-qiao Sun

Publisher: World Scientific

Published: 2013-09-25

Total Pages: 355

ISBN-13: 9814525510

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Analysis and control of time-delayed systems have been applied in a wide range of applications, ranging from mechanical, control, economic, to biological systems. Over the years, there has been a steady stream of interest in time-delayed dynamic systems, this book takes a snap shot of recent research from the world leading experts in analysis and control of dynamic systems with time delay to provide a bird's eye view of its development. The topics covered in this book include solution methods, stability analysis and control of periodic dynamic systems with time delay, bifurcations, stochastic dynamics and control, delayed Hamiltonian systems, uncertain dynamic systems with time delay, and experimental investigations of delayed structural control.

Chimera Patterns in Networks
Chimera Patterns in Networks

Author: Anna Zakharova

Publisher: Springer Nature

Published: 2020-03-09

Total Pages: 243

ISBN-13: 3030217140

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This is the first book devoted to chimera states - peculiar partial synchronization patterns in networks. Providing an overview of the state of the art in research on this topic, it explores how these hybrid states, which are composed of spatially separated domains of synchronized and desynchronized behavior, arise surprisingly in networks of identical units and symmetric coupling topologies. The book not only describes various types of chimeras, but also discusses the role of time delay, stochasticity, and network topology for these synchronization-desynchronization patterns. Moreover, it addresses the question of robustness and control of chimera states, which have various applications in physics, biology, chemistry, and engineering. This book is intended for researchers with a background in physics, applied mathematics, or engineering. Of great interest to specialists working on related problems, it is also a valuable resource for newcomers to the field and other scientists working on the control of spatio-temporal patterns.

Controlling Synchronization Patterns in Complex Networks
Controlling Synchronization Patterns in Complex Networks

Author: Judith Lehnert

Publisher: Springer

Published: 2015-11-06

Total Pages: 213

ISBN-13: 3319251155

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This research aims to achieve a fundamental understanding of synchronization and its interplay with the topology of complex networks. Synchronization is a ubiquitous phenomenon observed in different contexts in physics, chemistry, biology, medicine and engineering. Most prominently, synchronization takes place in the brain, where it is associated with several cognitive capacities but is - in abundance - a characteristic of neurological diseases. Besides zero-lag synchrony, group and cluster states are considered, enabling a description and study of complex synchronization patterns within the presented theory. Adaptive control methods are developed, which allow the control of synchronization in scenarios where parameters drift or are unknown. These methods are, therefore, of particular interest for experimental setups or technological applications. The theoretical framework is demonstrated on generic models, coupled chemical oscillators and several detailed examples of neural networks.

Emergence Of Dynamical Order: Synchronization Phenomena In Complex Systems
Emergence Of Dynamical Order: Synchronization Phenomena In Complex Systems

Author: Susanna C Manrubia

Publisher: World Scientific

Published: 2004-04-14

Total Pages: 359

ISBN-13: 9814482951

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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.

Advances in Neural Networks -- ISNN 2011
Advances in Neural Networks -- ISNN 2011

Author: Derong Liu

Publisher: Springer

Published: 2011-05-20

Total Pages: 667

ISBN-13: 3642211054

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The three-volume set LNCS 6675, 6676 and 6677 constitutes the refereed proceedings of the 8th International Symposium on Neural Networks, ISNN 2011, held in Guilin, China, in May/June 2011. The total of 215 papers presented in all three volumes were carefully reviewed and selected from 651 submissions. The contributions are structured in topical sections on computational neuroscience and cognitive science; neurodynamics and complex systems; stability and convergence analysis; neural network models; supervised learning and unsupervised learning; kernel methods and support vector machines; mixture models and clustering; visual perception and pattern recognition; motion, tracking and object recognition; natural scene analysis and speech recognition; neuromorphic hardware, fuzzy neural networks and robotics; multi-agent systems and adaptive dynamic programming; reinforcement learning and decision making; action and motor control; adaptive and hybrid intelligent systems; neuroinformatics and bioinformatics; information retrieval; data mining and knowledge discovery; and natural language processing.

Chaos and Complex Systems
Chaos and Complex Systems

Author: Stavros G. Stavrinides

Publisher: Springer Science & Business Media

Published: 2013-03-19

Total Pages: 559

ISBN-13: 364233914X

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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.