Mathematical Foundations of Neuroscience

Front Cover
Springer Science & Business Media, Jul 1, 2010 - Mathematics - 422 pages
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Chapter 1 The HodgkinHuxley Equations
1
Chapter 2 Dendrites
29
Chapter 3 Dynamics
49
Chapter 4 Th e Variety of Channels
77
Chapter 5 Bursting Oscillations
102
Chapter 6 Propagating Action Potentials
129
Chapter 7 Synaptic Channels
157
Chapter 8 Neural Oscillators Weak Coupling
171
Chapter 9 Neuronal Networks FastSlow Analysis
241
Chapter 10 Noise
285
Chapter 11 Firing Rate Models
331
Chapter 12 Spatially Distributed Networks
368
References
407
Index
419
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information