Dynamic Neuroscience

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.

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.

This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.

It is a well-known fact of neurophysiology that neuronal responses to identically presented stimuli are extremely variable. This variability has in the past often been regarded as "noise." At the single neuron level, interspike interval (ISI) histograms constructed during either spontaneous or stimulus evoked activity reveal a Poisson type distribution. These observations have been taken as evidence that neurons are intrinsically "noisy" in their firing properties. In fact, the use of averaging techniques, like post-stimulus time histograms (PSTH) or event-related potentials (ERPs) have largely been justified based on the presence of what was believed to be noise in the neuronal responses. More recent attempts to measure the information content of single neuron spike trains have revealed that a surprising amount of information can be coded in spike trains even in the presence of trial-to-trial variability. Multiple single unit recording experiments have suggested that variability formerly attributed to noise in single cell recordings may instead simply reflect system-wide changes in cellular response properties. These observations raise the possibility that, at least at the level of neuronal coding, the variability seen in single neuron responses may not simply reflect an underlying noisy process. They further raise the very distinct possibility that noise may in fact contain real, meaningful information which is available for the nervous system in information processing. To understand how neurons work in concert to bring about coherent behavior and its breakdown in disease, neuroscientists now routinely record simultaneously from hundreds of different neurons and from different brain areas, and then attempt to evaluate the network activities by computing various interdependence measures, including cross correlation, phase synchronization and spectral coherence. This book examines neuronal variability from theoretical, experimental and clinical perspectives.

"This book describes a new theoretical approach--Dynamic Field Theory (DFT)--that explains how people think and act"--

An examination of how widely distributed and specialized activities of the brain are flexibly and effectively coordinated. A fundamental shift is occurring in neuroscience and related disciplines. In the past, researchers focused on functional specialization of the brain, discovering complex processing strategies based on convergence and divergence in slowly adapting anatomical architectures. Yet for the brain to cope with ever-changing and unpredictable circumstances, it needs strategies with richer interactive short-term dynamics. Recent research has revealed ways in which the brain effectively coordinates widely distributed and specialized activities to meet the needs of the moment. This book explores these findings, examining the functions, mechanisms, and manifestations of distributed dynamical coordination in the brain and mind across different species and levels of organization. The book identifies three basic functions of dynamic coordination: contextual disambiguation, dynamic grouping, and dynamic routing. It considers the role of dynamic coordination in temporally structured activity and explores these issues at different levels, from synaptic and local circuit mechanisms to macroscopic system dynamics, emphasizing their importance for cognition, behavior, and psychopathology. Contributors Evan Balaban, György Buzsáki, Nicola S. Clayton, Maurizio Corbetta, Robert Desimone, Kamran Diba, Shimon Edelman, Andreas K. Engel, Yves Fregnac, Pascal Fries, Karl Friston, Ann Graybiel, Sten Grillner, Uri Grodzinski, John-Dylan Haynes, Laurent Itti, Erich D. Jarvis, Jon H. Kaas, J.A. Scott Kelso, Peter König, Nancy J. Kopell, Ilona Kovács, Andreas Kreiter, Anders Lansner, Gilles Laurent, Jörg Lücke, Mikael Lundqvist, Angus MacDonald, Kevan Martin, Mayank Mehta, Lucia Melloni, Earl K. Miller, Bita Moghaddam, Hannah Monyer, Edvard I. Moser, May-Britt Moser, Danko Nikolic, William A. Phillips, Gordon Pipa, Constantin Rothkopf, Terrence J. Sejnowski, Steven M. Silverstein, Wolf Singer, Catherine Tallon-Baudry, Roger D. Traub, Jochen Triesch, Peter Uhlhaas, Christoph von der Malsburg, Thomas Weisswange, Miles Whittington, Matthew Wilson

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.

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.