Why is my data is incorrect after looping?

Hello I'm working on this code that solves a set of differential equations and plots the solution and I'm varying the parameter 'k' from 1 to 4 to see how it changes the solution of the problem. For some reason after solving the differential equation inside the loop the u and v data is wrong. To further show this here is what the 'u' data looks like when run for k = 3:

And here is what the data looks like for k = 1:1:4:

As you can see the k=3 column has different data but it should be exactly the same. Can anyone figure out what is going on?

Here is the script:

%Clear command window and workspace
  clear 
  close all
  clc
  % Fitzhugh-Nagoma model parameters
  e=0.01; 
  k=1:1:4; a=0.1; 
  i = 0.001;
  figure(1);
  hold on
  u=zeros(500000,4);
  v=zeros(500000,4);
  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)));
      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 phase plot
figure(1);
upts=(-2:.05:2);
% unullpts=(k(1).*upts.*(upts-a).*(1-upts));
% vnullpts=upts;

for i = 1:numel(k)

unullpts=(k(i).*upts.*(upts-a).*(1-upts));

vnullpts=upts;

plot(upts,unullpts,'black',upts,vnullpts,'black');

hold on

end

Answer 1

[Torsten]

You must set the initial condition for u and v not only for u(1,1) and v(1,1), but for u(1,1:4) and v(1,1:4). And change all u(i) to u(i,:) and v(i) to v(i,:).

I think it is advisable to use a double loop (one from 1 to 4 and the other from 1 to 50000).

Best wishes

Torsten.