Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators
Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Author: Rico Berner

Publisher: Springer Nature

Published: 2021-05-31

Total Pages: 210

ISBN-13: 303074938X

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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.

Biological Clocks, Rhythms, and Oscillations
Biological Clocks, Rhythms, and Oscillations

Author: Daniel B. Forger

Publisher: MIT Press

Published: 2024-08-06

Total Pages: 369

ISBN-13: 0262552817

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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.

On Coexistence Patterns
On Coexistence Patterns

Author: Sindre W. Haugland

Publisher: Springer Nature

Published: 2023-02-20

Total Pages: 340

ISBN-13: 3031214986

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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.

Perspectives in Mathematical System Theory, Control, and Signal Processing
Perspectives in Mathematical System Theory, Control, and Signal Processing

Author: Jan C. Willems

Publisher: Springer Science & Business Media

Published: 2010-02-28

Total Pages: 391

ISBN-13: 3540939172

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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.

Dynamical Systems on Networks
Dynamical Systems on Networks

Author: Mason Porter

Publisher: Springer

Published: 2016-03-31

Total Pages: 91

ISBN-13: 3319266411

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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.

Brain Oscillations, Synchrony and Plasticity
Brain Oscillations, Synchrony and Plasticity

Author: Jos J. Eggermont

Publisher: Academic Press

Published: 2021-01-11

Total Pages: 270

ISBN-13: 0128204087

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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

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.

Routledge International Handbook of Memory Studies
Routledge International Handbook of Memory Studies

Author: Anna Lisa Tota

Publisher: Routledge

Published: 2015-09-16

Total Pages: 783

ISBN-13: 1134477562

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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.