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In the while loop, I am comparing the accuracy of Euler's and Midpoint methods (the methods themselves should be correct). If they differ by a certain amount, I reduce the step size by half and redo the calculation for that time point. Else, I update the indices and move on. Plot(t, x(:,4), t, y(:,4)) should gnerate a graph that portrays an action potential.

Somehow after dif hits the specified threshold, x, y, and dif stop to update. The step size keeps getting reduced and I get stuck in an infinite loop. Does anyone have any insights on what might have happened there? Any thought is appreciated!

dt = 0.08;

Vm = 0;

t(1)=0;

i_inj = 17;

%initial values for n, h, m, V

x = [0.317676914060697 0.596120753508460 0.0529324852572496 0]; %set first value to steady state to 0mV

y = [0.317676914060697 0.596120753508460 0.0529324852572496 0];

i = 1;

k = 1;

while t(k)<11

%Euler's method

x(i+1,:) = x(i,:)+dt.*derivs(t(k),x(i,:),i_inj);

%midpoint method

k1 = dt.*derivs(t(k),y(i,:),i_inj);

k2 = dt.*derivs(t(k)+0.5*dt,y(i,:)+0.5.*k1,i_inj);

y(i+1,:) = k2+y(i,:);

dif = abs(x(i+1,4)-y(i+1,4));

if (dif>=0.1)

dt = dt*0.5;

else

t(k+1) = dt+t(k);

i = i+1;

k = k+1;

end

end

function y = derivs(t,x,I_inj)

g_Kbar = 36;

E_K = -12;

g_Nabar = 120;

E_Na = 115;

Gm = 0.3;

V_rest = 10.613;

V=x(4);

if(V == 10)

alpha_n = 1/10;

else

alpha_n = (10-V)./(100*(exp(1-V/10)-1));

end

beta_n = 0.125*exp(-V/80);

n=x(1);

dndt = alpha_n*(1-n)-beta_n*n;

y(1) = dndt;

alpha_h = 0.07*exp(-V/20);

beta_h = 1/(exp(3-V/10)+1);

h=x(2);

dhdt = alpha_h*(1-h)-beta_h*h;

y(2) = dhdt;

if (V==25)

alpha_m = 1;

else

alpha_m = (25-V)/(10*(exp(2.5-V/10)-1));

end

beta_m = 4*exp(-V/18);

m=x(3);

dmdt = alpha_m*(1-m)-beta_m*m;

y(3) = dmdt;

if t>=1 && t<=1.5

dVdt = I_inj+g_Nabar.*m.^3.*h.*(E_Na-V)+g_Kbar.*n.^4.*(E_K-V)+Gm*(V_rest-V);

else

dVdt = g_Nabar.*m.^3.*h.*(E_Na-V)+g_Kbar.*n.^4.*(E_K-V)+Gm*(V_rest-V);

end

y(4) = dVdt;

end

Andy
on 26 Nov 2020

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