Dynamical Systems In Neuroscience
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| Author | : Eugene M. Izhikevich |
| Publisher | : MIT Press |
| Total Pages | : 459 |
| Release | : 2010-01-22 |
| Genre | : Medical |
| ISBN | : 0262514206 |
Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum—or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.
| Author | : E. M. Izhikevich |
| Publisher | : |
| Total Pages | : |
| Release | : 2005 |
| Genre | : |
| ISBN | : |
| Author | : Wulfram Gerstner |
| Publisher | : Cambridge University Press |
| Total Pages | : 591 |
| Release | : 2014-07-24 |
| Genre | : Computers |
| ISBN | : 1107060834 |
This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.
| Author | : Steven L. Brunton |
| Publisher | : Cambridge University Press |
| Total Pages | : 615 |
| Release | : 2022-05-05 |
| Genre | : Computers |
| ISBN | : 1009098489 |
A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
| Author | : Christoph Börgers |
| Publisher | : Springer |
| Total Pages | : 445 |
| Release | : 2017-04-17 |
| Genre | : Mathematics |
| ISBN | : 3319511718 |
This book is intended as a text for a one-semester course on Mathematical and Computational Neuroscience for upper-level undergraduate and beginning graduate students of mathematics, the natural sciences, engineering, or computer science. An undergraduate introduction to differential equations is more than enough mathematical background. Only a slim, high school-level background in physics is assumed, and none in biology. Topics include models of individual nerve cells and their dynamics, models of networks of neurons coupled by synapses and gap junctions, origins and functions of population rhythms in neuronal networks, and models of synaptic plasticity. An extensive online collection of Matlab programs generating the figures accompanies the book.
| Author | : Gregor Schöner |
| Publisher | : Oxford University Press |
| Total Pages | : 421 |
| Release | : 2016 |
| Genre | : Psychology |
| ISBN | : 0199300569 |
"This book describes a new theoretical approach--Dynamic Field Theory (DFT)--that explains how people think and act"--
| Author | : G. Bard Ermentrout |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2010-07-01 |
| Genre | : Mathematics |
| ISBN | : 0387877088 |
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.
| Author | : Zhe Chen |
| Publisher | : Springer |
| Total Pages | : 337 |
| Release | : 2017-12-27 |
| Genre | : Technology & Engineering |
| ISBN | : 3319719769 |
This book shows how to develop efficient quantitative methods to characterize neural data and extra information that reveals underlying dynamics and neurophysiological mechanisms. Written by active experts in the field, it contains an exchange of innovative ideas among researchers at both computational and experimental ends, as well as those at the interface. Authors discuss research challenges and new directions in emerging areas with two goals in mind: to collect recent advances in statistics, signal processing, modeling, and control methods in neuroscience; and to welcome and foster innovative or cross-disciplinary ideas along this line of research and discuss important research issues in neural data analysis. Making use of both tutorial and review materials, this book is written for neural, electrical, and biomedical engineers; computational neuroscientists; statisticians; computer scientists; and clinical engineers.
| Author | : Mikhail I. Rabinovich |
| Publisher | : MIT Press |
| Total Pages | : 371 |
| Release | : 2023-12-05 |
| Genre | : Medical |
| ISBN | : 0262549905 |
Experimental and theoretical approaches to global brain dynamics that draw on the latest research in the field. The consideration of time or dynamics is fundamental for all aspects of mental activity—perception, cognition, and emotion—because the main feature of brain activity is the continuous change of the underlying brain states even in a constant environment. The application of nonlinear dynamics to the study of brain activity began to flourish in the 1990s when combined with empirical observations from modern morphological and physiological observations. This book offers perspectives on brain dynamics that draw on the latest advances in research in the field. It includes contributions from both theoreticians and experimentalists, offering an eclectic treatment of fundamental issues. Topics addressed range from experimental and computational approaches to transient brain dynamics to the free-energy principle as a global brain theory. The book concludes with a short but rigorous guide to modern nonlinear dynamics and their application to neural dynamics.
| Author | : J. A. Scott Kelso |
| Publisher | : MIT Press |
| Total Pages | : 368 |
| Release | : 1995 |
| Genre | : Behavior |
| ISBN | : 9780262611312 |
foreword by Hermann Haken For the past twenty years Scott Kelso's research has focused on extending the physical concepts of self- organization and the mathematical tools of nonlinear dynamics to understand how human beings (and human brains) perceive, intend, learn, control, and coordinate complex behaviors. In this book Kelso proposes a new, general framework within which to connect brain, mind, and behavior.Kelso's prescription for mental life breaks dramatically with the classical computational approach that is still the operative framework for many newer psychological and neurophysiological studies. His core thesis is that the creation and evolution of patterned behavior at all levels--from neurons to mind--is governed by the generic processes of self-organization. Both human brain and behavior are shown to exhibit features of pattern-forming dynamical systems, including multistability, abrupt phase transitions, crises, and intermittency. Dynamic Patterns brings together different aspects of this approach to the study of human behavior, using simple experimental examples and illustrations to convey essential concepts, strategies, and methods, with a minimum of mathematics. Kelso begins with a general account of dynamic pattern formation. He then takes up behavior, focusing initially on identifying pattern-forming instabilities in human sensorimotor coordination. Moving back and forth between theory and experiment, he establishes the notion that the same pattern-forming mechanisms apply regardless of the component parts involved (parts of the body, parts of the nervous system, parts of society) and the medium through which the parts are coupled. Finally, employing the latest techniques to observe spatiotemporal patterns of brain activity, Kelso shows that the human brain is fundamentally a pattern forming dynamical system, poised on the brink of instability. Self-organization thus underlies the cooperative action of neurons that produces human behavior in all its forms.
