This is part 2 of the Hodgkin-Huxley theory and modeling work.

Below are the Hodgkin-Huxley equations for membrane excitability. Create an *.ode file to implement these equations. Run some simulations varying the applied current, hand in a print out showing the working model. We will make use of this *.ode file more after the mid-term.

v′ = (-1/C)*(I_Na + I_K + I_L - I_app)
m′ = α_m(V)*(1 - m) - β_m(V)*m
h′ = α_h(V)*(1 - h) - β_h(V)*h
n′ = α_n(V)*(1 - n) - β_n(V)*n

initial V = -65.08
initial m = 0.0568
initial h= 0.568
initial n = 0.318

α_h(V) = 0.0027*e^-v/20
α_m(V) = 0.1*(V + 40)/(1 - e^-(v+40)/10)
α_n(V) = 0.01*(V + 55)/(1-e^-(v+55)/10)
β_h(V) = 1/(1+e^-(v+35)/10)
β_m(V) = 0.108*e^-v/18
β_n(V) = 0.055*e^-v/80

I_Na = g_Na-max*m³*h*(V - E_Na)
I_K = g_K-max*n⁴*(V - E_K)
I_L = g_L*(V - E_L)

C = 1
g_K-max = 36
g_L = 0.3
g_Na-max = 120
E_K = -77
E_L = -54.4
E_Na = 50

You have several options for I_app; you can implement a heavyside step function or a simple steady current. At first just make I_app a parameter and try values from 0 to 10 and see how the HH system responds.