Morris-Lescar Model of Membranes with Multiple Ion Channels

Application of various depolarizing currents to barnacle muscle fibers produces spikes or oscillations for some values of the applied current. The Morris–Lescar model, which is a simplified version of the Hodgkin–Huxley model, involves a fast-activating calcium current; a slow potassium current, which is coupled to the calcium current; and a passive leak. The nonlinear simultaneous differential equations display bifurcation corresponding to these modes of behavior for various values of the relevant parameters.

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An increase in the applied current first produces a steady state in the membrane voltage, then a transient spike, and finally continued oscillation. (Since the oscillations begin at nonzero frequencies, they are termed Type II.) Increasing the initial voltage causes a similar sequence of behavior (termed excitability), as does varying the relaxation rate. Each of these changes may be seen to be reflected as a bifurcation in the phase plane representation.
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