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Tutorials in Mathematical Biosciences I

Mathematical Neuroscience

  • Textbook
  • © 2005

Overview

Authors:
  1. Alla Borisyuk
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  2. Avner Friedman
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  3. Bard Ermentrout
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  4. David Terman
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1860)

Part of the book sub series: Mathematical Biosciences Subseries (LNMBIOS)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-IX
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  2. Introduction to Neurons

    • Avner Friedman
    Pages 1-20

  3. An Introduction to Dynamical Systems and Neuronal Dynamics

    • David Terman
    Pages 21-68

  4. Neural Oscillators

    • Bard Ermentrout
    Pages 69-106

  5. Physiology and Mathematical Modeling of the Auditory System

    • Alla Borisyuk
    Pages 107-168

  6. Back Matter

    Pages 169-170
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Keywords

About this book

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.

Reviews

From the reviews:

"Each paper ends with a valuable bibliography. The volume introduces some basic theories on computational neuroscience. I recommend this volume as a very good book in mathematical neurosciences." (Ioan A. Rus, Zentralblatt MATH, Vol. 1062 (13), 2005)

"The present volume, a collection of four articles, introduces some basic theories of mathematical and computational neuroscience. … I found the book to be a very good tutorial in mathematical neuroscience, well written and organized. … The core is a compilation of mathematical results from a rich bibliography … . In conclusion, I strongly recommend this volume to any graduate student, postdoctoral fellow or researcher moving to the field of theoretical neuroscience." (Rodica Curtu, Mathematical Reviews, Issue 2007 d)

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