Morris-Lecar Model

Simplified version of Hodgkin Huxley Model, becuase it is 2 dimensional instead of 4 dimensional we can visualize it in a Phase Plane.

$$C\frac{dV}{dt}={\bar{g}}_{K}n(E_K-V)+{\bar{g}}_{Na}{m}_{\infty }(E_K-V)+I_{leak}$$ $$\frac{dn}{dt}=\frac{n_{\infty }-n}{{\tau }_n}$$

Where:

Variables

• V : membrane potential
• N : recovery variable: the probability that the K+ channel is conducting

Parameters/Constants

• $I$ : applied current
• $C$ : membrane capacitance
• _g_L, _g_Ca, _g_K : leak, Ca++, and K+ conductances through membranes channel
• _V_L, _V_Ca, _V_K : equilibrium potential of relevant ion channels
• $V_1,V_2,V_3,V_4$: tuning parameters for steady state and time constant
• $\varphi$: reference frequency

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Great example is a sub critical Andronov Hopf Bifurcation