Download or read book Neuronal Dynamics written by Wulfram Gerstner and published by Cambridge University Press. This book was released on 2014-07-24 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.

Download or read book Frequency domain Approach To Hopf Bifurcation Analysis Continuous Time delayed Systems written by Franco Sebastian Gentile and published by World Scientific. This book was released on 2019-10-07 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of an effective frequency-domain approach, based on systems control theory, to compute and analyze several types of standard bifurcation conditions for general continuous-time nonlinear dynamical systems. A very rich pictorial gallery of local bifurcation diagrams for such nonlinear systems under simultaneous variations of several system parameters is presented. Some higher-order harmonic balance approximation formulas are derived for analyzing the oscillatory dynamics in small neighborhoods of certain types of Hopf and degenerate Hopf bifurcations.The frequency-domain approach is then extended to the large class of delay-differential equations, where the time delays can be either discrete or distributed. For the case of discrete delays, two alternatives are presented, depending on the structure of the underlying dynamical system, where the more general setting is then extended to the case of distributed time-delayed systems. Some representative examples in engineering and biology are discussed.

Download or read book An Introduction to the Mathematics of Neurons written by F. C. Hoppensteadt and published by Cambridge University Press. This book was released on 1997-06-28 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the signal processing aspects of neural networks. It begins with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, and then proceeds to applications. These applications include small networks of neurons, such as those used in control of warm-up and flight in moths and control of respiration during exercise in humans. Next, a theory of mnemonic surfaces is developed and studied and material on pattern formation and cellular automata is presented. Finally, large networks are studied, such as the thalamus-reticular complex circuit, believed to be involved in focusing attention, and the development of connections in the visual cortex. Additional material is also provided about nonlinear wave propagation in networks. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life sciences.

Download or read book Advances in Neural Information Processing Systems 13 written by Todd K. Leen and published by MIT Press. This book was released on 2001 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the 2000 Neural Information Processing Systems (NIPS) Conference.The annual conference on Neural Information Processing Systems (NIPS) is the flagship conference on neural computation. The conference is interdisciplinary, with contributions in algorithms, learning theory, cognitive science, neuroscience, vision, speech and signal processing, reinforcement learning and control, implementations, and diverse applications. Only about 30 percent of the papers submitted are accepted for presentation at NIPS, so the quality is exceptionally high. These proceedings contain all of the papers that were presented at the 2000 conference.

Download or read book Neural Organization written by Michael A. Arbib and published by MIT Press. This book was released on 1998 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Neural Organization, Arbib, Erdi, and Szentagothai integrate structural, functional, and dynamical approaches to the interaction of brain models and neurobiologcal experiments. Both structure-based "bottom-up" and function- based "top-down" models offer coherent concepts by which to evaluate the experimental data. The goal of this book is to point out the advantages of a multidisciplinary, multistrategied approach to the brain.Part I of Neural Organization provides a detailed introduction to each of the three areas of structure, function, and dynamics. Structure refers to the anatomical aspects of the brain and the relations between different brain regions. Function refers to skills and behaviors, which are explained by means of functional schemas and biologically based neural networks. Dynamics refers to the use of a mathematical framework to analyze the temporal change of neural activities and synaptic connectivities that underlie brain development and plasticity--in terms of both detailed single-cell models and large-scale network models.In part II, the authors show how their systematic approach can be used to analyze specific parts of the nervous system--the olfactory system, hippocampus, thalamus, cerebral cortex, cerebellum, and basal ganglia--as well as to integrate data from the study of brain regions, functional models, and the dynamics of neural networks. In conclusion, they offer a plan for the use of their methods in the development of cognitive neuroscience."

Download or read book From Structure to Function in Neuronal Networks Effects of Adaptation Time Delays and Noise written by Serhiy Yanchuk and published by Frontiers Media SA. This book was released on 2022-05-06 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Proceedings of the 1995 World Congress on Neural Networks written by Joseph T. DeWitte and published by Routledge. This book was released on 2019-02-21 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Centered around major topic areas of both theoretical and practical importance, the World Congress on Neural Networks provides its registrants -- from a diverse background encompassing industry, academia, and government -- with the latest research and applications in the neural network field.

Download or read book Neural Fields written by Stephen Coombes and published by Springer. This book was released on 2014-06-17 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neural field theory has a long-standing tradition in the mathematical and computational neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan, Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright and Haken. Since then, much progress has been made in both, the development of mathematical and numerical techniques and in physiological refinement und understanding. In contrast to large-scale neural network models described by huge connectivity matrices that are computationally expensive in numerical simulations, neural field models described by connectivity kernels allow for analytical treatment by means of methods from functional analysis. Thus, a number of rigorous results on the existence of bump and wave solutions or on inverse kernel construction problems are nowadays available. Moreover, neural fields provide an important interface for the coupling of neural activity to experimentally observable data, such as the electroencephalogram (EEG) or functional magnetic resonance imaging (fMRI). And finally, neural fields over rather abstract feature spaces, also called dynamic fields, found successful applications in the cognitive sciences and in robotics. Up to now, research results in neural field theory have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. There is no comprehensive collection of results or reviews available yet. With our proposed book Neural Field Theory, we aim at filling this gap in the market. We received consent from some of the leading scientists in the field, who are willing to write contributions for the book, among them are two of the founding-fathers of neural field theory: Shun-ichi Amari and Jack Cowan.

Download or read book Phase Response Curves in Neuroscience written by Nathan W. Schultheiss and published by Springer Science & Business Media. This book was released on 2011-12-22 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by response to a workshop at the 2008 OCNS meeting, this book tracks advances in the application of phase response (PR) analysis to the study of electrically excitable cells, focusing on applications of PR analysis in the computational neurosciences.

Download or read book Neuroinformatics of Large Scale Brain Modelling written by John David Griffiths and published by Frontiers Media SA. This book was released on 2022-11-10 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Coherent Behavior in Neuronal Networks written by Krešimir Josic and published by Springer Science & Business Media. This book was released on 2009-08-22 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent experimental research advances have led to increasingly detailed descriptions of how networks of interacting neurons process information. With these developments, it has become clear that dynamic network behaviors underlie information processing, and that the observed activity patterns cannot be fully explained by simple concepts such as synchrony and phase locking. These new insights raise significant challenges and offer exciting opportunities for experimental and theoretical neuroscientists. Coherent Behavior in Neuronal Networks features a review of recent research in this area from some of the world’s foremost experts on systems neuroscience. The book presents novel methodologies and interdisciplinary perspectives, and will serve as an invaluable resource to the research community. Highlights include the results of interdisciplinary collaborations and approaches as well as topics, such as the interplay of intrinsic and synaptic dynamics in producing coherent neuronal network activity and the roles of globally coherent rhythms and oscillations in the coordination of distributed processing, that are of significant research interest but have been underrepresented in the review literature. With its cutting-edge mathematical, statistical, and computational techniques, this volume will be of interest to all researchers and students in the field of systems neuroscience.

Download or read book Handbook of Brain Connectivity written by Viktor K. Jirsa and published by Springer. This book was released on 2007-08-16 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our contemporary understanding of brain function is deeply rooted in the ideas of the nonlinear dynamics of distributed networks. Cognition and motor coordination seem to arise from the interactions of local neuronal networks, which themselves are connected in large scales across the entire brain. The spatial architectures between various scales inevitably influence the dynamics of the brain and thereby its function. But how can we integrate brain connectivity amongst these structural and functional domains? Our Handbook provides an account of the current knowledge on the measurement, analysis and theory of the anatomical and functional connectivity of the brain. All contributors are leading experts in various fields concerning structural and functional brain connectivity. In the first part of the Handbook, the chapters focus on an introduction and discussion of the principles underlying connected neural systems. The second part introduces the currently available non-invasive technologies for measuring structural and functional connectivity in the brain. Part three provides an overview of the analysis techniques currently available and highlights new developments. Part four introduces the application and translation of the concepts of brain connectivity to behavior, cognition and the clinical domain.

Download or read book Differential Equations with Applications to Biology written by Shigui Ruan and published by American Mathematical Soc.. This book was released on with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from the International Conference held in Halifax, NS in July 1997. Funded by The Fields Institute and Le Centre de Recherches Mathématiques, the conference was held in honor of the retirement of Professors Lynn Erbe and Herb I. Freedman (University of Alberta). Featured topics include ordinary, partial, functional, and stochastic differential equations and their applications to biology, epidemiology, neurobiology, physiology and other related areas. The 41 papers included in this volume represent the recent work of leading researchers over a wide range of subjects, including bifurcation theory, chaos, stability theory, boundary value problems, persistence theory, neural networks, disease transmission, population dynamics, pattern formation and more. The text would be suitable for a graduate or advanced undergraduate course study in mathematical biology. Features: An overview of current developments in differential equations and mathematical biology. Authoritative contributions from over 60 leading worldwide researchers. Original, refereed contributions.

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 Basal Ganglia X Proceedings of the 10th Triennial Meeting of the International Basal Ganglia Society written by Charles J. Wilson and published by Frontiers E-books. This book was released on with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles describing research on the basic, pre-clinical and clinical neuroscience of the basal ganglia written by attendees of the 10th Triennial Meeting of the International Basal Ganglia Society (IBAGS) that was held June 20-24th, 2010 at the Ocean Place Resort in Long Branch, New Jersey, USA. For each of the preceding 9 IBAGS meetings, the meeting proceedings were published conventionally as a volume in the Advances in Behavioral Biology series. These volumes were expensive, were published only in very small quantities, had very limited availability to both basal ganglia researchers and the general neuroscience community, were not available on-line and the articles contained in each were not indexed in online searchable databases. Now, for the first time, IBAGS is taking full advantage of modern innovations in scientific publication and publishing IBAGS X as a Research Topics issue of Frontiers in Systems Neuroscience. The issue will be available on-line and is fully indexed by searchable databases including PubMed. Articles will include reports on the latest research on the anatomy and neurophysiology of single neurons and functional circuitry in the striatum, globus pallidus, subthalamic nucleus and substantia nigra as well as the latest data on animal models of basal ganglia dysfunction as well as behavioral and clinical studies in human patients.

Download or read book Differential Equations and Control Theory written by Z. Deng and published by CRC Press. This book was released on 2020-11-25 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents the proceedings from the International Conference on Differential Equations and Control Theory, held recently in Wuhan, China. It provides an overview of current developments in a range of topics including dynamical systems, optimal control theory, stochastic control, chaos, fractals, wavelets and ordinary, partial, functional and stochastic differential equations.

Download or read book Mathematical Foundations of Neuroscience written by G. Bard Ermentrout and published by Springer Science & Business Media. This book was released on 2010-07-01 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.