How to correctly change a variable from a single number to an array.

Hello, I oringinally wrote this matlab code to model the FitzHugh-Nagumo action potential. Now I'm trying to modify the model to get a string of action potentials. To do this I need to change all the state variables to array shown below:

These equations:

% Fitzhugh-Nagoma model parameters
e=0.03; k=3; a=0.05; 

Are changed to this:

% Fitzhugh-Nagoma model parameters
e=[0.03 0.03]; k=[3 3]; a=[0.05 0.05];  

However when I do this the code doesn't run. Can somebody explain what needs to change in the rest of the code to get it to work? Thanks a lot!

%Clear command window and workspace
clear 
close all
clc

% Fitzhugh-Nagoma model parameters
e=[0.03 0.03]; k=[3 3]; a=[0.05 0.05]; 
i = 0.001;

figure(1);
hold on

u=zeros(100000,1);
v=zeros(100000,1);
t=zeros(100000,1);

% Initial conditions:
u(1)=0.6;
v(1)=0.0;

t(1)=0;
dt=0.001;

%==========================================================================
% Forvard Euler Method, for soluing the ODE
%==========================================================================

for i=1:1:500000
    
    t(i+1)=t(i)+dt;
    u(i+1) = u(i)+ dt*((1/e)*((k*u(i)*(u(i)-a)*(1-u(i)))-v(i)));
    v(i+1) = v(i)+ dt*(u(i)-v(i));
      
end

% Getting the plot

figure(1);
plot(t,u)
legend('u','Trajectory')
title('Time Series Plot')
xlabel('Time')
ylabel('u')
xlim([0 5])

Answer 1

[Jan]

e = [0.03 0.035]; k = [3 3]; a = [0.05 0.05]; 
n = 500000;
u = zeros(n, 2);
v = zeros(n, 2);
t = zeros(n, 1);

% Initial conditions:
u(1, :) = 0.6;
v(1, :) = 0.0;
t(1)    = 0;
dt      = 0.00001;

% Forward Euler Method, for soluing the ODE
for i = 1:n - 1
    t(i+1) = t(i) + dt;
    u(i+1, :) = u(i, :) + dt * ((1 ./ e) .* ...
       ((k .* u(i, :) .* (u(i, :) - a) .* (1 - u(i, :))) - v(i, :)));
    v(i+1, :) = v(i, :) + dt * (u(i, :) - v(i, :));
end

figure;
plot(t, u)

All you have to do is to define u and v as matrices instead of vectors and to change \ and * to the elementwise operations .\ and .* . Then acces the subvectors as u(i, :) instead of u(i).

[Stephen23]

And read this:

https://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html