MATLAB: How to plot for a matrix

Question

Hello, in this code I am varying the parameter k from 1 to 4 and I get four different sets of numbers for u and v. I want to plot all sets of these numbers on the same graph so I should get multiple lines. However, when I run it, it only plots for one set of values. Does anyone know how to fix this? Thanks!

%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(:)=0.3;
v(:)=0.0;
t(1)=0;
dt=0.001;
%==========================================================================

% Forvard Euler Method, for soluing the ODE
%==========================================================================
for k=1:4
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
end
% Getting the phase plot
figure(1);
upts=(-2:.05:2);
unullpts=(k*upts.*(upts-a).*(1-upts));
vnullpts=upts;
plot(upts,unullpts,'black',upts,vnullpts,'black');
xlabel('u'); ylabel('v');
axis([-1 2 -1.5 5]);
plot(u,v,'b')
title('Nullcline Plot')
xlabel('u')
ylabel('v')

Answer 1

You for to use the index k from the outer loop:

% Fitzhugh-Nagoma model parameters
e = 0.01;
k = 1:1:4;
a = 0.1; 
i = 0.001;
u=zeros(5000,4);
v=zeros(5000,4);
t=zeros(1000,1);
% Initial conditions:
u(:)=0.3;
v(:)=0.0;
t(1)=0;
dt=0.001;
%
for k=1:4
    for i=1:1:5000
        t(i+1)=t(i)+dt;
        u(i+1,k) = u(i,k)+ dt.*((1/e).*((k.*(u(i,k).*(u(i,k)-a).*(1-u(i,k))))-v(i)));
        v(i+1,k) = v(i,k)+ dt*(u(i,k)-v(i,k));
    end  %    ^        ^           ^      ^ you forgot to use |k|.                            
end
plot(t,u,'r', t,v,'b')

Gives: