Solving ODE system on matlab

I am trying to solve a system ODEs with no specific initial values and I am not sure how to go about it. Here is what I have so far. I'm trying to use ODE45 and solve with several initial conditions to have an idea of how the system ( with 3 equations) behaves. Thank you in advance!!

function Untitled
t= 1:0.5:50;
a=.004;
b=0.5;
c=1;
initial=[a b c];
[~,y]= ode45(@model,t,initial)
plot3(y(1),y(2),y(3));
end

function y=model(~,y)
y=zeros(3,1);
dy(1)=y(1)*(1-y(1)-2*y(2)-y(3)/2);
dy(2)=y(2)*(1-y(2)-2*y(3)-y(1)/2);
dy(3)=y(3)*(1-y(3)-2*y(1)-y(2)/2);
end

Answer 1

[James Tursa]

Your plot3 only picks off three points to plot ... it does not plot all of the results. Also, your model derivative function sets y to 0 and then returns that, rather than returning the dy you calculate. So with those changes maybe you can use this:

function Untitled
t= 1:0.5:50;
a=.004;
b=0.5;
c=1;
initial=[a b c];
[~,y]= ode45(@model,t,initial);
figure; plot3(y(:,1),y(:,2),y(:,3));grid on
figure; plot(t,y(:,1),t,y(:,2),t,y(:,3));grid on
end

function dy=model(~,y)
dy=zeros(3,1);
dy(1)=y(1)*(1-y(1)-2*y(2)-y(3)/2);
dy(2)=y(2)*(1-y(2)-2*y(3)-y(1)/2);
dy(3)=y(3)*(1-y(3)-2*y(1)-y(2)/2);
end