Download or read book Patterns of Synchrony and Disorder in Networks of Coupled Oscillators written by Oleh Omelʹchenko and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Synchronization of coupled oscillators manifests itself in many natural and man-made systems, including cyrcadian clocks, central pattern generators, laser arrays, power grids, chemical and electrochemical oscillators, only to name a few. The mathematical description of this phenomenon is often based on the paradigmatic Kuramoto model, which represents each oscillator by one scalar variable, its phase. When coupled, phase oscillators constitute a high-dimensional dynamical system, which exhibits complex behaviour, ranging from synchronized uniform oscillation to quasiperiodicity and chaos. The corresponding collective rhythms can be useful or harmful to the normal operation of various systems, therefore they have been the subject of much research. Initially, synchronization phenomena have been studied in systems with all-to-all (global) and nearest-neighbour (local) coupling, or on random networks. However, in recent decades there has been a lot of interest in more complicated coupling structures, which take into account the ...
Download or read book Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators written by Rico Berner and published by Springer Nature. This book was released on 2021-05-31 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this thesis is the interplay of synchrony and adaptivity in complex networks. Synchronization is a ubiquitous phenomenon observed in different contexts in physics, chemistry, biology, neuroscience, medicine, socioeconomic systems, and engineering. Most prominently, synchronization takes place in the brain, where it is associated with cognitive capacities like learning and memory, but is also a characteristic of neurological diseases like Parkinson and epilepsy. Adaptivity is common in many networks in nature and technology, where the connectivity changes in time, i.e., the strength of the coupling is continuously adjusted depending upon the dynamic state of the system, for instance synaptic neuronal plasticity in the brain. This research contributes to a fundamental understanding of various synchronization patterns, including hierarchical multifrequency clusters, chimeras and other partial synchronization states. After a concise survey of the fundamentals of adaptive and complex dynamical networks and synaptic plasticity, in the first part of the thesis the existence and stability of cluster synchronization in globally coupled adaptive networks is discussed for simple paradigmatic phase oscillators as well as for a more realistic neuronal oscillator model with spike-timing dependent plasticity. In the second part of the thesis the interplay of adaptivity and connectivity is investigated for more complex network structures like nonlocally coupled rings, random networks, and multilayer systems. Besides presenting a plethora of novel, sometimes intriguing patterns of synchrony, the thesis makes a number of pioneering methodological advances, where rigorous mathematical proofs are given in the Appendices. These results are of interest not only from a fundamental point of view, but also with respect to challenging applications in neuroscience and technological systems.
Download or read book Biological Clocks Rhythms and Oscillations written by Daniel B. Forger and published by MIT Press. This book was released on 2024-08-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.
Download or read book Synchrony and Chaos in Coupled Oscillators and Neural Networks written by Sridhar Raghavachari and published by . This book was released on 1999 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Controlling Synchronization Patterns in Complex Networks written by Judith Lehnert and published by Springer. This book was released on 2015-11-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Synchronization in Oscillatory Networks written by Grigory V. Osipov and published by Springer Science & Business Media. This book was released on 2007-08-10 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as electric power grids, lasers or even the heart muscle, to name but a few. The book is conceived as an introduction to the field for graduate students in physics and applied mathematics as well as being a compendium for researchers from any field of application interested in quantitative models.
Download or read book On Coexistence Patterns written by Sindre W. Haugland and published by Springer Nature. This book was released on 2023-02-20 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about coexistence patterns in ensembles of globally coupled nonlinear oscillators. Coexistence patterns in this respect are states of a dynamical system in which the dynamics in some parts of the system differ significantly from those in other parts, even though there is no underlying structural difference between the different parts. In other words, these asymmetric patterns emerge in a self-organized manner. As our main model, we use ensembles of various numbers of Stuart-Landau oscillators, all with the same natural frequency and all coupled equally strongly to each other. Employing computer simulations, bifurcation analysis and symmetry considerations, we uncover the mechanism behind a wide range of complex patterns found in these ensembles. Our starting point is the creation of so-called chimeras, which are subsequently treated within a new and broader context of related states.
Download or read book Chimera States in Complex Networks written by Eckehard Schöll and published by Frontiers Media SA. This book was released on 2020-01-03 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Chimera Patterns in Networks written by Anna Zakharova and published by Springer Nature. This book was released on 2020-03-09 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Perspectives in Mathematical System Theory Control and Signal Processing written by Jan C. Willems and published by Springer Science & Business Media. This book was released on 2010-02-28 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift, published on the occasion of the sixtieth birthday of Yutaka - mamoto (‘YY’ as he is occasionally casually referred to), contains a collection of articles by friends, colleagues, and former Ph.D. students of YY. They are a tribute to his friendship and his scienti?c vision and oeuvre, which has been a source of inspiration to the authors. Yutaka Yamamoto was born in Kyoto, Japan, on March 29, 1950. He studied applied mathematics and general engineering science at the Department of Applied Mathematics and Physics of Kyoto University, obtaining the B.S. and M.Sc. degrees in 1972 and 1974. His M.Sc. work was done under the supervision of Professor Yoshikazu Sawaragi. In 1974, he went to the Center for Mathematical System T- ory of the University of Florida in Gainesville. He obtained the M.Sc. and Ph.D. degrees, both in Mathematics, in 1976 and 1978, under the direction of Professor Rudolf Kalman.
Download or read book Dynamical Systems on Networks written by Mason Porter and published by Springer. This book was released on 2016-03-31 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models, including spreading models for social and biological contagions. The authors focus especially on “simple” situations that are analytically tractable, because they are insightful and provide useful springboards for the study of more complicated scenarios. This tutorial, which also includes key pointers to the literature, should be helpful for junior and senior undergraduate students, graduate students, and researchers from mathematics, physics, and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks. Mason A. Porter is Professor of Nonlinear and Complex Systems at the Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, UK. He is also a member of the CABDyN Complexity Centre and a Tutorial Fellow of Somerville College. James P. Gleeson is Professor of Industrial and Applied Mathematics, and co-Director of MACSI, at the University of Limerick, Ireland.
Download or read book 15th Chaotic Modeling and Simulation International Conference written by Christos H. Skiadas and published by Springer Nature. This book was released on 2023-07-10 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings of 15th CHAOS2022 International Conference highlights recent developments in nonlinear, dynamical, and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and Engineering Sciences. The principal aim of CHAOS2022 International Conference is to expand the development of the theories of the applied nonlinear field, the methods, empirical data and computer techniques as well as the best theoretical achievements of chaotic theory. CHAOS2022 Conference provides a forum for bringing together the various groups working in the area of Nonlinear and Dynamical Systems, Chaotic theory and Application to exchange views and report research findings.
Download or read book Multiscale Models of Brain Disorders written by Vassilis Cutsuridis and published by Springer Nature. This book was released on 2019-10-11 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on our current understanding of brain dynamics in various brain disorders (e.g. epilepsy, Alzheimer’s and Parkinson’s disease) and how the multi-scale, multi-level tools of computational neuroscience can enhance this understanding. In recent years, there have been significant advances in the study of the dynamics of the disordered brain at both the microscopic and the macroscopic levels. This understanding can be furthered by the application of multi-scale computational models as integrative principles that may link single neuron dynamics and the dynamics of local and distant brain regions observed using human EEG, ERPs, MEG, LFPs and fMRI. Focusing on the computational models that are used to study movement, memory and cognitive disorders as well as epilepsy and consciousness related diseases, the book brings together physiologists and anatomists investigating cortical circuits; cognitive neuroscientists studying brain dynamics and behavior by means of EEG and functional magnetic resonance imaging (fMRI); and computational neuroscientists using neural modeling techniques to explore local and large-scale disordered brain dynamics. Covering topics that have a significant impact on the field of medicine, neuroscience and computer science, the book appeals to a diverse group of investigators.
Download or read book Brain Oscillations Synchrony and Plasticity written by Jos J. Eggermont and published by Academic Press. This book was released on 2021-01-11 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brain Oscillations, Synchrony and Plasticity: Basic Principles and Application to Auditory-Related Disorders discusses the role of brain oscillations, especially with respect to the auditory system and how those oscillations are measured, change over the lifespan, and falter leading to a variety of psychiatric and neurological disorders. The book begins with a description of these cortical rhythm oscillations and how they function in both the normal and pathological brain. It explains how these oscillations are important to auditory, executive and attention brain networks and how they relate to the development, production and deterioration of speech and language. In addition, treatment of malfunctioning cortical rhythms are reviewed using neuromodulation, such as transcranial magnetic, direct current, random noise, and alternating current stimulation, as well as focused ultrasound. The book concludes by describing the potential role of oscillations in dyslexia, autism, schizophrenia and Alzheimer’s disease. Introduces readers to brain imaging methods such as structural and functional magnetic resonance imaging, EEG and magnetoencephalography, in the study of brain oscillations, synchrony and networks of the normal and pathological brain Highlights the role of brain oscillations in perception and cognition, in particular with respect to the auditory system, speech and language Describes lifespan changes, from preterm to senescence, of brain oscillations, brain networks and how they relate to the development and deterioration of speech and language Explains the effects of hearing loss on neural network change in the auditory and non-auditory networks such as the default mode-, the salience-, the executive- and attention networks Illustrates the breakdown of network connections in auditory-related disorders such as tinnitus and in psychiatric disorders with a strong auditory, speech and language component
Download or read book Synchronization in Networks of Nonlinear Circuits written by Mattia Frasca and published by Springer. This book was released on 2018-03-10 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses synchronization in networks of coupled systems. It illustrates the main aspects of the phenomenon through concise theoretical results and code, allowing readers to reproduce them and encouraging readers to pursue their own experimentation. The book begins by introducing the mathematical representation of nonlinear circuits and the code for their simulation. This is followed by a brief account of the concept of the complex network, which describes the main aspects of complex networks and the main model types, with a particular focus on the code used to study and reproduce the models. The focus then shifts to the process through which independent nonlinear circuits that follow different trajectories without coupling share some properties of their motion: synchronization. The authors present the main techniques for studying synchronization in complex networks, including the major measures, the stability properties and control techniques. The book then moves on to advanced topics in synchronization of complex networks by examining forms of synchronization in which not all the units share the same trajectory, namely chimera states, clustering synchronization, and relay and remote synchronization. Simple codes for experimentation with these topics and control methods are also provided. In closing, the book addresses the problem of synchronization in time-varying networks.
Download or read book Routledge International Handbook of Memory Studies written by Anna Lisa Tota and published by Routledge. This book was released on 2015-09-16 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Routledge International Handbook of Memory Studies offers students and researchers original contributions that comprise the debates, intersections and future courses of the field. It is divided in six themed sections: 1)Theories and Perspectives, 2) Cultural artefacts, Symbols and Social practices, 3) Public, Transnational, and Transitional Memories 4) Technologies of Memory, 5) Terror, Violence and Disasters, 6) and Body and Ecosystems. A strong emphasis is placed on the interdisciplinary breadth of Memory Studies with contributions from leading international scholars in sociology, anthropology, philosophy, biology, film studies, media studies, archive studies, literature and history. The Handbook addresses the core concerns and foundations of the field while indicating new directions in Memory Studies.
Download or read book Network Approaches to Diseases of the Brain written by Matt T. Bianchi and published by Bentham Science Publishers. This book was released on 2012 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers novel approaches using networks and oscillations and it will serve as a catalyst for translating these exciting advancements into the clinical arena. This collection of articles aims to accelerate the widespread clinical translation of network approaches by providing practical information accessible to clinicians in neurology and psychiatry - fields that are uniquely poised to implement these developments in clinical treatment of brain diseases. It should be a useful resource for researchers and clinicians in neurology and psychiatry.
