Tutorials in Mathematical Biosciences I: Mathematical Neuroscience

✍ Scribed by Alla Borisyuk, Avner Friedman, Bard Ermentrout, David Terman (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2005
• Tongue: English
• Leaves: 178
• Series: Lecture Notes in Mathematics 1860 Mathematical Biosciences Subseries
• Edition: 1
• Category: Library

✦ Synopsis

This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems.

✦ Table of Contents

Introduction to Neurons....Pages 1-20
An Introduction to Dynamical Systems and Neuronal Dynamics....Pages 21-68
Neural Oscillators....Pages 69-106
Physiology and Mathematical Modeling of the Auditory System....Pages 107-168

✦ Subjects

Mathematical Biology in General; Ordinary Differential Equations; Partial Differential Equations; Computational Mathematics and Numerical Analysis; Neurobiology; Computer Appl. in Life Sciences