edited by Stephen Coombes (The University of Nottingham, UK) & Paul C Bressloff (University of Utah, USA)

Table of Contents (102k)
Preface (91k)
Chapter 1: The Development of the Hindmarsh-Rose Model for Bursting (316k)

Neurons in the brain communicate with each other by transmitting sequences of electrical spikes or action potentials. One of the major challenges in neuroscience is to understand the basic physiological mechanisms underlying the complex spatiotemporal patterns of spiking activity observed during normal brain functioning, and to determine the origins of pathological dynamical states such as epileptic seizures and Parkinsonian tremors. A second major challenge is to understand how the patterns of spiking activity provide a substrate for the encoding and transmission of information, that is, how do neurons compute with spikes? It is likely that an important element of both the dynamical and computational properties of neurons is that they can exhibit bursting, which is a relatively slow rhythmic alternation between an active phase of rapid spiking and a quiescent phase without spiking. This book provides a detailed overview of the current state-of-the-art in the mathematical and computational modeling of bursting, with contributions from many of the leading researchers in the field.

• Bursting at the Single Cell Level:
  • The Development of the Hindmarshrose Model for Bursting (J Hindmarsh & P Cornelius)
  • Negative Calcium Feedback: The Road from Chay-Keizer (R Bertram & A Sherman)
  • Autoregulation of Bursting of AVP Neurons of the Rat Hypothalamus (P Roper et al.)
  • Bifurcations in the Fast Dynamics of Neurons: Implications for Bursting (J Guckenheimer et al.)
  • Bursting in 2-Compartment Neurons: A Case Study of the Pinsky-Rinzel Model (A Bose & V Booth)
  • Ghostbursting: The Role of Active Dendrites in Electrosensory Processing (C R Laing & B Doiron)
• Bursting at the Network Level:
  • Analysis of Circuits Containing Bursting Neurons Using Phase Resetting Curves (C Canavier)
  • Bursting in Coupled Cell Systems (M Golubitsky et al.)
  • Modulatory Effects of Coupling on Bursting Maps (G de Vries)
  • Beyond Synchronization: Modulatory and Emergent Effects of Coupling in Square-Wave Bursting (G de Vries & A Sherman)
  • Bursting in Excitatory Neural Networks (J Tabak & J Rinzel)
  • Oscillatory Bursting Mechanisms in Respiratory Pacemaker Neurons and Networks (R Butera et al.)
  • Geometric Analysis of Bursting Networks (J Best & D Terman)
  • Elliptic Bursters, Depolarization Block, and Waves (B Ermentrout et al.)