MATLAB: LorenzSystem, ode23

ode23

Hi, I get a question to model the LorenzSystem. It has
dx/dt = 10(y-x)  
dy/dt = -xz+28x-y
dz/dt = xy-8z/3
Setting the initial value x = 1; y = 2; z =3. It should get a graph like this. But mine is so weird.
function chaotic
 clc;clear;
 %LorenzSystem
 y0=[1;2;3];
 soln = ode23(@f,[0 100],y0)
 t = linspace(0,100,300);
 y(:,1)=deval(soln,t,1); 
 y(:,2)=deval(soln,t,2); 
 y(:,3)=deval(soln,t,3); 
   figure
   plot3(y(:,1),y(:,2),y(:,3));
   hold on;grid on;
   end
   function dxdt = f(t,x)
   dxdt=[0;0;0];
   dxdt(1) = 10*(x(2)-x(1));
   dxdt(2) = -x(1)*x(3)+28 * x(1)- x(2);
   dxdt(3) = x(1)*x(2)-8*x(3)/3;
   end

Best Answer

It’s always best not to ‘overthink’ problems (and I admit that I’ve don that so often, I’ve lost count).
This works:
% Lorenz System
f = @(t,x) [10*(x(2)-x(1));  -x(1).*x(3)+28 .* x(1)- x(2);  x(1).*x(2)-8*x(3)/3];
y0=[1;2;3];
[t,y] = ode23(f,[0 100],y0);
figure(1)
plot3(y(:,1),y(:,2),y(:,3));
grid on
Note: This is all your code, I just copy-pasted it to an anonymous function, and did a few edits.
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