Dynamical Systems in Neuroscience:

Introduction 23Figure 1.19: Richard FitzHugh in 1984.If only life was so simple!The geometrical analysis of neuronal models was further developed, among others,by Izhikevich (2000), who stressed the integrator and resonator modes of operationand made connections to other neuro-computational properties.The neuroscience and mathematics parts of this book are standard, though manyconnections are new. We point to the literature sources at the end of each chapter.Among many outstanding books on computational neuroscience, we especially recommendSpikes, Decisions, and Actions by Wilson (1999), Biophysics of Computation byKoch (1999), Theoretical Neuroscience by Dayan and Abbott (2001), and Foundationsof Cellular Neurophysiology by Johnston and Wu (1995). The present monographcomplements these excellent books in the sense that it is more ambitious, focused,and thorough in dealing with neurons as dynamical systems. Though the views inthis monograph may be biased by the author’s philosophy and taste, the payoffs inunderstanding neuronal dynamics are immense, provided that the reader has enoughpatience and perseverance to follow the author’s line of thought.NEURON simulation environment is described by Hines (1989) (http://www.neuron.yale.edu),GENESIS environment is described by Bower and Beeman (1995) (http://www.genesis-sim.org),XPP environment is described by Ermentrout (2002). The author of this book usesMATLAB (version 6.5 for Windows), which has become a standard computational toolin science and engineering (MATLAB is registered trademark of The MathWorks, Inc.;see http://www.mathworks.com).