Tutorials in Mathematical Biosciences I

Mathematical Neuroscience

  • Authors
  • Alla Borisyuk
  • Avner Friedman
  • Bard Ermentrout
  • David Terman

Part of the Lecture Notes in Mathematics book series (LNM, volume 1860)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Avner Friedman
    Pages 1-20
  3. Bard Ermentrout
    Pages 69-106
  4. Back Matter
    Pages 169-170

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.


Computational Neuroscience Cortex anatomy auditory system dynamical systems neural oscillations neuronal dynamics neurons physiology

Bibliographic information