Abstract
The nervous system functions to encode, process, store and transmit information. To perform these tasks, neurons have evolved sophisticated means of generating electrical and chemical signals. The goals of this chapter are to provide a more detailed mathematical description of neuronal excitability and to introduce several mathematical tools based upon the theory of nonlinear dynamical systems that can be used to analyze neuronal excitability. These mathematical tools (e.g., phase plane analysis, bifurcation theory) provide graphical or geometric representations of the system dynamics and can be used to understand, predict and interpret biophysical features such as threshold phenomena and oscillatory and bursting behavior, as well as the mechanisms of bistability and hysteresis. Such analyses can provide novel insights into the capabilities of individual neurons to process and store information.
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