create a Simulink model from this matlab code Show the results and model Step $1$: Model Initialization

Create a new Simulink model.

Add a Voltage Source block to represent the stimulus current $($Istim$).$ You can find this block under the Sources library in Simulink.

Add a Sum block to sum the ionic currents. You can find this block under the Math Operations library in Simulink.

Add a Scope block to visualize the membrane potential $($V$)$ and gating variables $($m$,$ n$,$ h$).$ You can find this block under the Sinks library in Simulink.

Step $2$: Parameter Setup

Set the parameters of the Hodgkin$-$Huxley Neuron block to match the equations and parameters of the Hodgkin$-$Huxley model. This includes setting the membrane capacitance $($Cm$),$ maximum conductances $($gNa$,$ gK$,$ gL$),$ Nernst potentials $($ENa$,$ EK$,$ EL$),$ and rate constants $($alpha and beta$).$

Step $3$: Implementing the Hodgkin$-$Huxley Equations

Use a MATLAB Function block to implement the Hodgkin$-$Huxley equations.

Already included in the code Create a MATLAB function that calculates the membrane potential $($V$)$ and gating variable derivatives $($dm$/$dt$,$ dn$/$dt$,$ dh$/$dt$)$ based on the current membrane potential and gating variable values.

Use the MATLAB function to calculate the derivatives in the MATLAB Function block.

Step $4$: Connecting Blocks

Connect the output of the MATLAB Function block to the input of the Scope block to visualize the simulation results.

Connect the output of the Voltage Source block to the input of the Sum block, and connect the output of the Sum block to the input of the MATLAB Function block.

Step $5$: Simulation and Analysis

Run the simulation and observe the membrane potential and gating variable dynamics over time.

Analyze the behavior of the neuron in response to different stimulus currents and parameter values.$\%$ Sample inputs

V $=-65$; $\%$ Membrane potential $($mV$)$

m $=0\mathrm{.}05$; $\%$ Gating variable m

n $=0\mathrm{.}31$; $\%$ Gating variable n

h $=0\mathrm{.}6$; $\%$ Gating variable h

Istim $=10$; $\%$ Stimulus current $($uA$/$cm$^2)$

Cm $=1$; $\%$ Membrane capacitance $($uF$/$cm$^2)$

gNa $=120$; $\%$ Maximum sodium conductance $($mS$/$cm$^2)$

gK $=36$; $\%$ Maximum potassium conductance $($mS$/$cm$^2)$

gL $=0\mathrm{.}3$; $\%$ Leak conductance $($mS$/$cm$^2)$

ENa $=115$; $\%$ Sodium Nernst potential $($mV$)$

EK $=-12$; $\%$ Potassium Nernst potential $($mV$)$

EL $=10\mathrm{.}6$; $\%$ Leak Nernst potential $($mV$)$

$\%$ Call the function

$[$dV$,$ dm$,$ dn$,$ dh$]=$ hodgkin$\_$huxley$\_$model$($V$,$ m$,$ n$,$ h$,$ Istim, Cm$,$ gNa, gK$,$ gL$,$ ENa, EK$,$ EL$)$;

function $[$dV$,$ dm$,$ dn$,$ dh$]=$ hodgkin$\_$huxley$\_$model$($V$,$ m$,$ n$,$ h$,$ Istim, Cm$,$ gNa, gK$,$ gL$,$ ENa, EK$,$ EL$)$

$\%$ Constants

$[$~$]=-65$; $\%$ Resting membrane potential $($mV$)$

$\%$ Sodium channel kinetics

alpha$\_$m $=0\mathrm{.}1*($V$+40)/(1-$exp$(-($V$+40)/10))$;

beta$\_$m $=4*$exp$(-($V$+65)/18)$;

alpha$\_$h $=0\mathrm{.}07*$exp$(-($V$+65)/20)$;

beta$\_$h $=1/(1+$exp$(-($V$+35)/10))$;

$\%$ Potassium channel kinetics

alpha$\_$n $=0\mathrm{.}01*($V$+55)/(1-$exp$(-($V$+55)/10))$;

beta$\_$n $=0\mathrm{.}125*$exp$(-($V$+65)/80)$;

$\%$ Membrane currents

I$\_$Na $=$ gNa$*($m$^3)*$h$*($V$-$ENa$)$;

I$\_$K $=$ gK$*($n$^4)*($V$-$EK$)$;

I$\_$L $=$ gL$*($V$-$EL$)$;

$\%$ Membrane potential derivative

dV $=($Istim $-$ I$\_$Na $-$ I$\_$K $-$ I$\_$L$)/$ Cm;

$\%$ Gating variable derivatives

dm $=$ alpha$\_$m$*(1-$m$)-$ beta$\_$m$*$m;

dn $=$ alpha$\_$n$*(1-$n$)-$ beta$\_$n$*$n;

dh $=$ alpha$\_$h$*(1-$h$)-$ beta$\_$h$*$h;

end