title: Methods in Neuronal Modeling - 2nd Edition: From Ions to Networks (Computational Neuroscience)
author: Idan Segev
description: <P>"An admirable concentration of expertise on state-of-the-art neuronalmodeling techniques&mdash;a must on the bookshelf of computationalneuroscientists and theoretical neurobiologists." <B>Wolf Singer </B>, M.D., Ph.D., Max-Planck-Institute for Brain Research</P>
zlib_text: INTRODUCTION 
  CNN is an acronym for either Cellular Neural Network when used in the 
  context of brain science, or Cellular Nonlinear Network when used in the 
  context of coupled dynamical systems. A CNN is defined by two mathemat­
  ical constructs: 
  1. A spatially discrete collection of continuous nonlinear dynamical systems 
  called cells, where information can be encrypted into each cell via three 
  independent variables called input, threshold, and initial state. 
  2. A coupling law relating one or more relevant variables of each cell dj 
  to all neighbor cells Cki located within a prescribed sphere of influence 
  Sij(r) of radius r, centered at 
  dj. 
  In the special case where the CNN consists of a homogeneous array, and 
  where its cells have no inputs, no thresholds, and no outputs, and where the 
  sphere of influence extends only to the nearest neighbors (i.e. r = 1), the 
  CNN reduces to the familiar concept of a nonlinear lattice. 
  Part I of this three-part exposition (reprinted from a 