lorentz simulation error what is the error please help

clear 
ti = 0; % set the initial value of t 
tf = 130; % set the final value of t 
dt = 0.01; 
% set the step size 
xo = 1.0; yo = 1.0; zo = 1.0; 
% set the initial conditions (arbitrarily) 
t = [ti : dt : tf]; 
% creating a vector of the nodal points 
N = length(t); 
% calculate the number of nodes 
r(:,1) = [xo ; yo ; zo]; 
% creating a vector with the initial conditions 
for i = 1: N-1 
    k1 = dt * f( t(i) , r(:,i) ); 
    k2 = dt * f( t(i)+dt/2 , r(:,i)+k1/2); 
    k3 = dt * f( t(i)+dt/2 , r(:,i)+k2/2);
    k4 = dt * f( t(i)+dt , r(:,i)+k3); 
    r(:,i+1) = r(:,i)+(k1+2*k2+2*k3+k4)/6; 
end 
figure(1),plot(t,r(1,:),t,r(2,:),t,r(3,:))

figure(2),plot3(r(1,:),r(2,:),r(3,:)),grid on 

clear t 
x=r(1,3002:N)'; 
y=r(2,3002:N)';
z=r(3,3002:N)'; 
clear r 
figure(3),plot3(x,y,z),grid on

function [rdot] = f (t,r)
sigma = 10; 
rho = 28; beta = 8/3; 
rdot=zeros(3,1); 
rdot(1) = sigma*(r(2)-r(1)); 
rdot(2) = rho*r(1)-r(2)-r(1)*r(3); 
rdot(3) = r(1)*r(2)-beta*r(3); 
end             

IM getting error message saying 'f' requires more input arguments to run :f(t,r) it says enter input arguments what is the error please and how it should be wrriten many thanks

[Torsten]

Works for me (see above).

[Numan]

thanks a lot for clearing this out.Im actually simulating the chen system with its chen attractor using same principle but im getting error

the parameters and equations for the chen system is dx/dt = alpha * x - y * z;

dy/dt = beta * y + x * z;

dz/dt = sigma * z + (x * y) / 3;

with sigma=-0.38 beta=-10 and ALPHA =5

many thanks to you

my code for chen system is

clear

ti = 0; % set the initial value of t

tf = 130; % set the final value of t

dt = 0.01;

% set the step size

xo = 5.0; yo = 10.0; zo = 10.0;

% set the initial conditions (arbitrarily)

t = [ti : dt : tf];

% creating a vector of the nodal points

N = length(t);

% calculate the number of nodes

r(:,1) = [xo ; yo ; zo];

% creating a vector with the initial conditions

for i = 1: N-1

k1 = dt * f( t(i) , r(:,i) );

k2 = dt * f( t(i)+dt/2 , r(:,i)+k1/2);

k3 = dt * f( t(i)+dt/2 , r(:,i)+k2/2);

k4 = dt * f( t(i)+dt , r(:,i)+k3);

r(:,i+1) = r(:,i)+(k1+2*k2+2*k3+k4)/6;

end

figure(1),plot(t,r(1,:),t,r(2,:),t,r(3,:))

figure(2),plot3(r(1,:),r(2,:),r(3,:)),grid on

clear t

x=r(1,3002:N)';

y=r(2,3002:N)';

z=r(3,3002:N)';

clear r

figure(3),plot3(x,y,z),grid on

function [rdot] = f (t,r)

sigma = -0.38;

alpha = 5; beta = -10;

rdot=zeros(3,1);

rdot(1) = alpha * x - y * z;

rdot(2) = beta * y + x * z;

rdot(3) = sigma * z + (x * y) / 3;

end

im getting this error Unrecognized function or variable 'x'.

Error in untitled8>f (line 34)

rdot(1) = alpha*x-y*z;

Error in untitled8 (line 15)

k1 = dt * f( t(i) , r(:,i) );

[Sam Chak]

Hi @Numan

Because in this f(t, r) function, the rdot() operations involve x, but no defined variable 'x' or recognized function 'x' is found throughout the code.

function [rdot] = f(t, r)

sigma = -0.38;

alpha = 5; beta = -10;

rdot=zeros(3,1);

rdot(1) = alpha * x - y * z;

rdot(2) = beta * y + x * z;

rdot(3) = sigma * z + (x * y) / 3;

end

Answer 1

[Sam Chak]

Hi @Numan

I have fixed the code in f(t, r) function, by adding the definitions for x, y, z. Check if the results are expected.

ti = 0; % set the initial value of t 
tf = 130; % set the final value of t 
dt = 0.01; 
% set the step size 
xo = 5.0; yo = 10.0; zo = 10.0; 
% set the initial conditions (arbitrarily) 
t = [ti : dt : tf]; 
% creating a vector of the nodal points 
N = length(t); 
% calculate the number of nodes 
r(:,1) = [xo ; yo ; zo]; 
% creating a vector with the initial conditions 
for i = 1: N-1 
    k1 = dt * f( t(i) , r(:,i) ); 
    k2 = dt * f( t(i)+dt/2 , r(:,i)+k1/2); 
    k3 = dt * f( t(i)+dt/2 , r(:,i)+k2/2);
    k4 = dt * f( t(i)+dt , r(:,i)+k3); 
    r(:,i+1) = r(:,i)+(k1+2*k2+2*k3+k4)/6; 
end 
figure(1),plot(t,r(1,:),t,r(2,:),t,r(3,:))

figure(2),plot3(r(1,:),r(2,:),r(3,:)),grid on 

clear t 
x=r(1,3002:N)'; 
y=r(2,3002:N)';
z=r(3,3002:N)'; 
clear r 
figure(3),plot3(x,y,z),grid on

function [rdot] = f (t, r)
    sigma   = -0.38; 
    alpha   = 5; 
    beta    = -10; 
    x       = r(1);     
    y       = r(2);
    z       = r(3);
    rdot    = zeros(3,1);
    rdot(1) = alpha * x - y * z;
    rdot(2) = beta * y + x * z;
    rdot(3) = sigma * z + (x * y) / 3;
end           

[Numan]

woow many thanks i got it too..can you please tell me how to edit my code so as my 3D plot axes are of 3 different colour please

[Numan]

After i hav ecompleted the simulation of chen system i will need to compute the fractal dimension also which i have no cllue..ay help please

[Torsten]

@Numan

Here is my help to make you capable to help yourself:

https://matlabacademy.mathworks.com/details/matlab-onramp/gettingstarted

[Numan]

THANKS ALOT Torsten.i will defo give it a try Have you got any idea how to compute its capacity dimension please for chen systen i would be gratfeful

[Torsten]

This is not a MATLAB question - thus not suited for this forum.

[Numan]

I mean computing the fractal dimension using box to box method is not matlab?

[Torsten]

No. But if you have MATLAB code for this method and it shows errors for the above system, we can try to help you. That's why I suggested to pass the free MATLAB online tutorial.

[Numan]

% Compute Fractal Dimension (Capacity Dimension)

epsilon = 0.1:0.1:10; % Range of epsilon values

N_eps = length(epsilon); % Number of epsilon values

N_points = zeros(N_eps, 1); % Number of points within epsilon distance

for i = 1:N_eps

for j = 1:length(x)

dist = sqrt((x - x(j)).^2 + (y - y(j)).^2 + (z - z(j)).^2);

N_points(i) = N_points(i) + sum(dist < epsilon(i));

end

end

% Compute the capacity dimension

log_N = log(N_points);

log_eps = log(epsilon);

coeffs = polyfit(log_eps, log_N, 1);

fractal_dim = coeffs(1);

disp("Fractal Dimension (Capacity Dimension): " + fractal_dim);

oh sorry i have my code for capacity dimension for my chen system but it wont work unfortunately..thank you a lot