How to have multiple lines on a graph for different values of a parameter.

Hello,

I'm trying to vary the parameter 'k' from 0 to 4 in this code. However, there is an error because the blue lines in the plot should not be shooting out to the right. Can anyone see what I am doing wrong?

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(:)=0.6;
v(:)=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(:)*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

[madhan ravi]

EDITED

   %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(:)=0.6;
  v(:)=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;
plot(upts,unullpts,'black',upts,vnullpts,'black');
axis([-1 2 -1.5 5]);
 hold on
plot(-u,-v,'b')
unullpts=(k(2).*upts.*(upts-a).*(1-upts));
vnullpts=upts;
plot(upts,unullpts,'m');
unullpts=(k(3).*upts.*(upts-a).*(1-upts));
vnullpts=upts;
plot(upts,unullpts,'r');
unullpts=(k(4).*upts.*(upts-a).*(1-upts));
vnullpts=upts;
plot(upts,unullpts,'g');

title('Nullcline Plot')
xlabel('u')
ylabel('v')

[Westin Messer]

Thank you! And do you know how to get the different lines to show up on the graph? Because it's still only plotting one of the solutions.

[madhan ravi]

v(k,i+1)

[Westin Messer]

Where does that go?

[madhan ravi]

How many graphs you expect and which one you want to plot against which??

[madhan ravi]

See edited answer

[Westin Messer]

I want to plot the u matrix against the v matrix like in line 39:

plot(u,v,'b')

[madhan ravi]

plot(u(:,1),v(:,1))

hold on

plot(u(:,2),v(:,2))

plot(u(:,3),v(:,3))

plot(u(:,4),v(:,4))

[madhan ravi]

The above comment plot u and v against each other resulting in 4 different plots

[madhan ravi]

If your zoom in the arrowhead you will see 4 different unique colours which represents u and v

[Westin Messer]

Thanks. Is there any way I can put that in some kind of loop? For example, if I wanted to do 20 different values of k I wouldn't have to write the plot line 20 times.

[madhan ravi]

for i = 1:numel(k)

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

vnullpts=upts;

plot(upts,unullpts,'m');

hold on

end

The above does the same work what you want