ABSTRACT
This chapter introduces the generalized Hodgkin-Huxley formalism for modeling voltage-dependent and time-dependent changes in membrane conductance that underlie neural excitability. It examines the Morris-Lecar model, a simple two-conductance system that exhibits a variety of interesting dynamic properties including oscillation, bistability, and threshold behavior. Phase space analysis is a powerful technique for developing insights and intuition into the behavior of nonlinear systems. The chapter illustrates the use of phase space techniques for analyzing the dynamic properties of this simple model of electrical excitability in a single neuron. A. L. Hodgkin and A. F. Huxley proposed that a segment of nerve membrane could be modeled by an electrical equivalent circuit. In general, the ionic conductances gj are not constant, but can depend on other biophysical parameters like membrane voltage or ionic concentrations. Each membrane channel can be thought of as containing a number of gates. Each gate can be in one of two states, "permissive" or "non-permissive.".
