MATLAB: How can i call array elements in a plot3 function

communicationlorenzMATLAB

s=10; %sigma b=8/3; %beta r=28; %rho h=0.003; %time step size x=0; %initialize x y=1; z=0; f=zeros(1,3); f=[x y z]; for t=0:h:100 k1_x=a*(y-x); k2_x=a*(y-x)+(k1_x*h*0.5); k3_x=a*(y-x)+(k2_x*h*0.5); k4_x=a*(y-x)+(k3_x*h); x_n=x+(k1_x+(2*k2_x)+(2*k3_x)+(k4_x))*h/6; %x_n is xn+1
    k1_y=x*(r-z)-y;
    k2_y=(x*(r-z)-y)+k1_y*h*0.5;
    k3_y=(x*(r-z)-y)+k2_y*h*0.5;
    k4_y=(x*(r-z)-y)+k3_y*h*0.5;
    y_n=y+(k1_y+(2*k2_y)+(2*k3_y)+(k4_y))*h/6; %y_n is yn+1, the next value of y
    k1_z=x*y-b*z;
    k2_z=(x*y-b*z)+k1_z*h*0.5;
    k3_z=(x*y-b*z)+k2_z*h*0.5;
    k4_z=(x*y-b*z)+k3_z*h*0.5;
    z_n=z+(k1_z+(2*k2_z)+(2*k3_z)+(k4_z))*h/6; %z_n is zn+1 the next value of z
    x=x_n;
    y=y_n;
    z=z_n;
end; plot3(x,y,z); grid on; xlabel('x'); ylabel('y'); zlabel('z'); title('Lorenz attractor');
The plot comes back empty.

Best Answer

s=10;b=8/3; r=28;h=0.003; a=28
x=0;y=1; z=0; f=zeros(1,3); f=[x y z]; 
k=1;
for t=0:h:100 
    k1_x=a*(y(k)-x(k));
    k2_x=a*(y(k)-x(k))+(k1_x*h*0.5);
    k3_x=a*(y(k)-x(k))+(k2_x*h*0.5);
    k4_x=a*(y(k)-x(k))+(k3_x*h);
    x(k+1)=x(k)+(k1_x+2*k2_x+2*k3_x+k4_x)*h/6; 
    k1_y=x(k)*(r-z(k))-y(k);
    k2_y=(x(k)*(r-z(k))-y(k))+k1_y*h*0.5;
    k3_y=(x(k)*(r-z(k))-y(k))+k2_y*h*0.5;
    k4_y=(x(k)*(r-z(k))-y(k))+k3_y*h*0.5;
    y(k+1)=y(k)+(k1_y+(2*k2_y)+(2*k3_y)+(k4_y))*h/6; 
    k1_z=x(k)*y(k)-b*z(k);
    k2_z=(x(k)*y(k)-b*z(k))+k1_z*h*0.5;
    k3_z=(x(k)*y(k)-b*z(k))+k2_z*h*0.5;
    k4_z=(x(k)*y(k)-b*z(k))+k3_z*h*0.5;
    z(k+1)=z(k)+(k1_z+(2*k2_z)+(2*k3_z)+(k4_z))*h/6; 
    k=k+1;
end
    plot3(x,y,z); grid on; xlabel('x'); ylabel('y');
    zlabel('z'); title('Lorenz attractor');
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