Mathematical Foundations of Neuroscience - Couverture rigide

Ermentrout, G. Bard; Terman, David H.

Couverture rigide

ISBN 10 : 038787707X ISBN 13 : 9780387877075

Editeur : Springer-Verlag New York Inc., 2010

Synopsis

One cansay that the ?eld ofcomputationalneurosciencestarted with the 1952paper ofHodgkinandHuxleyin whichtheydescribe, throughnonlinearpartialdifferential equations, the genesis of the action potential in the giant axon of the squid. These equations and the methods that arose from this combination of modeling and - periments have since formed the basis for nearly every subsequent model for active cells.TheHodgkin Huxleymodelandahostofsimpli?edequationsthatarederived fromit haveinspiredthedevelopmentofnewandbeautifulmathematics.Dynamical systems and computational methods are now being used to study activity patterns in a variety of neuronal systems. It is becoming increasingly recognized, by both experimentalists and theoreticians, that issues raised in neuroscience and the ma- ematical analysis of neuronal models provide unique interdisciplinary collaborative research and educational opportunities. This book is motivated by a perceived need for an overview of how dynamical systems and computational analysis have been used in understanding the types of models that come out of neuroscience. Our hope is that this will help to stimulate an increasing number of collaborations between mathematicians and other th- reticians, looking for interesting and relevant problems in applied mathematics and dynamical systems, and neuroscientists, looking for new ways to think about the biological mechanisms underlying experimental data. The book arose out of several courses that the authors have taught. One of these is a graduate course in computational neuroscience that has students from the d- ciplines of psychology, mathematics, computer science, physics, and neuroscience."

A propos du livre

Présentation de l'éditeur

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. "This excellent 422 page hardcover publication is an accessible and concise monograph . . . Mathematical Foundations is a timely contribution that will prove useful to mathematics graduate students and faculty interested in the application of dynamical systems theory to cellular and systems neuroscience . . . welcome addition to the ped

Détails de l'édition

• Éditeur: Springer-Verlag New York Inc.
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 038787707X
• ISBN 13: 9780387877075
• Reliure: Relié
• Nombre de pages: 422
• Coordonnées du fabricant: non disponible
• Personne responsable: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Allemagne