How can I use Lorenz Attractor code?

Hi everyone!

i want to simulate Lorenz Attractor using the script I found in Matlab File Exchange by Moiseev Igor. But I do not know how to input my parametes here.

my parameters are

sigma= 10

beta=8/3;

rho=28

x=5

y=5

z=5

and i want to integrate it from t=0 to 20.

function [x,y,z] = lorenz(rho, sigma, beta, initV, T, eps)

% LORENZ Function generates the lorenz attractor of the prescribed values

% of parameters rho, sigma, beta

%

% [X,Y,Z] = LORENZ(RHO,SIGMA,BETA,INITV,T,EPS)

% X, Y, Z - output vectors of the strange attactor trajectories

% RHO - Rayleigh number

% SIGMA - Prandtl number

% BETA - parameter

% INITV - initial point

% T - time interval

% EPS - ode solver precision

%

% Example.

% [X Y Z] = lorenz(28, 10, 8/3);

% plot3(X,Y,Z);

if nargin<3

error('MATLAB:lorenz:NotEnoughInputs','Not enough input arguments.');

end

if nargin<4

eps = 0.000001;

T = [0 25];

initV = [0 1 1.05];

end

options = odeset('RelTol',eps,'AbsTol',[eps eps eps/10]);

[T,X] = ode45(@(T,X) F(T, X, sigma, rho, beta), T, initV, options);

plot3(X(:,1),X(:,2),X(:,3));

axis equal;

grid;

title('Lorenz attractor');

xlabel('X'); ylabel('Y'); zlabel('Z');

x = X(:,1);

y = X(:,2);

z = X(:,3);

return

end

function dx = F(T, X, sigma, rho, beta)

% Evaluates the right hand side of the Lorenz system

% x' = sigma*(y-x)

% y' = x*(rho - z) - y

% z' = x*y - beta*z

% typical values: rho = 28; sigma = 10; beta = 8/3;

dx = zeros(3,1);

dx(1) = sigma*(X(2) - X(1));

dx(2) = X(1)*(rho - X(3)) - X(2);

dx(3) = X(1)*X(2) - beta*X(3);

return

end

Thank you and have a nice day.

[KALYAN ACHARJYA]

Is these x,y,z are same as function output [x,y,z]?

x=5
y=5
z=5

Function

function [x,y,z] = lorenz(rho, sigma, beta, initV, T, eps)
%.........^^^^
end

[Darwin Tuazon]

I'm confused to function [x,y,z] = lorenz(rho, sigma, beta, initV, T, eps)

Parameters values are sigma= 10; beta=8/3; rho=28;

and my intial values is x=5; y=5; z=5

Answer 1

[Sulaymon Eshkabilov]

Hi,

You were not executing the codes properly. Here is a single code that associates both scripts into one. Now it is much simpler.

sigma=10; beta=8/3; ro=28;  % Your data
ICs=[5, 5, 5];              % Your data   
t=[0, 20];
OPTs = odeset('reltol', 1e-6, 'abstol', 1e-8);
[time, fOUT]=ode45(@(t, x)([-sigma*x(1)+sigma*x(2);  -x(2)-x(1).*x(3); -beta*x(3)+x(1).*x(2)-beta*ro]), t, ICs, OPTs);
close all 
figure 
plot3(fOUT(:,1), fOUT(:,2), fOUT(:,3)), grid
xlabel('x(t)'), ylabel('y(t)'), zlabel('z(t)')
title('LORENZ functions x(t) vs. y(t) vs. z(t)')
axis tight
figure 
comet3(fOUT(:,1), fOUT(:,2), fOUT(:,3))
figure
subplot(311)
plot(time, fOUT(:,1), 'b','linewidth', 3), grid minor
title 'LORENZ functions x(t), y(t), z(t)', xlabel 'time', ylabel 'x(t)'
subplot(312)
plot( time', fOUT(:,2), 'r', 'linewidth', 2 ), grid minor
xlabel 'time', ylabel 'y(t)'
subplot(313)
plot(time, fOUT(:,3),'k', 'linewidth', 2), grid minor, xlabel 'time', ylabel 'z(t)'

figure
plot(fOUT(:,1), fOUT(:,2), 'b', 'linewidth', 1.5)
grid minor, title('LORENZ functions'), xlabel('x(t)'), ylabel 'y(t)'
axis square

figure
plot(fOUT(:,1), fOUT(:,3), 'k', 'linewidth', 1.5)
grid minor, title('LORENZ functions'), xlabel('x(t)'), ylabel 'z(t)'
axis square

figure
plot(fOUT(:,2), fOUT(:,3), 'm', 'linewidth', 1.5)
grid minor, title('LORENZ functions'), xlabel('y(t)'), ylabel 'z(t)'
axis square

Good luck.

[Ghofran Khaled]

https://ww2.mathworks.cn/matlabcentral/answers/1586374-how-i-create-improved-lorenz-code

colud you help me please

[Sulaymon Eshkabilov]

Post your question here in: www.mathworks.com

[Ghofran Khaled]

I posted it before and didn't get an answer

The question is in this link

https://ww2.mathworks.cn/matlabcentral/answers/1586514-how-can-i-create-improved-lorenz-mapping-code?s_tid=srchtitle_how%20can%20i%20create%20improved%20lorenz%20code_1

Answer 2

[Sulaymon Eshkabilov]

Hi Darwin,

Here is my version of the Lorenz Atractor simulation code:

function  df = LORENZ_sys_1ODE(~, x)
% HELP: Lorenz Functions
% dx/dt=-sigma*x+sigma*y;
% dy/dt=- y-x*z;
% dz/dt=-beta*z+x*y-beta*ro;
sigma=10; beta=8/3; ro=28;
% ICs: x(0)=5; y(0)=5; z(0)=5;  % Your ICs
df=[-sigma*x(1)+sigma*x(2); ...
    -x(2)-x(1).*x(3);...
    -beta*x(3)+x(1).*x(2)-beta*ro];
end

Run this part to simulate the whole system

ICs=[5, 5, 5];  % Your data
t=[0, 20];      % Your simulation space
OPTs = odeset('reltol', 1e-6, 'abstol', 1e-8);  % Optional ODE options set up
[time, fOUT]=ode45(@LORENZ_sys_1ODE, t, ICs, OPTs);
close all 
figure 
plot3(fOUT(:,1), fOUT(:,2), fOUT(:,3)), grid
xlabel('x(t)'), ylabel('y(t)'), zlabel('z(t)')
title('LORENZ functions x(t) vs. y(t) vs. z(t)')
axis tight
figure 
comet3(fOUT(:,1), fOUT(:,2), fOUT(:,3))
figure
subplot(311)
plot(time, fOUT(:,1), 'b','linewidth', 3), grid minor
title 'LORENZ functions x(t), y(t), z(t)', xlabel 'time', ylabel 'x(t)'
subplot(312)
plot( time', fOUT(:,2), 'r', 'linewidth', 2 ), grid minor
xlabel 'time', ylabel 'y(t)'
subplot(313)
plot(time, fOUT(:,3),'k', 'linewidth', 2), grid minor, xlabel 'time', ylabel 'z(t)'

figure
plot(fOUT(:,1), fOUT(:,2), 'b', 'linewidth', 1.5)
grid minor, title('LORENZ functions'), xlabel('x(t)'), ylabel 'y(t)'
axis square

figure
plot(fOUT(:,1), fOUT(:,3), 'k', 'linewidth', 1.5)
grid minor, title('LORENZ functions'), xlabel('x(t)'), ylabel 'z(t)'
axis square

figure
plot(fOUT(:,2), fOUT(:,3), 'm', 'linewidth', 1.5)
grid minor, title('LORENZ functions'), xlabel('y(t)'), ylabel 'z(t)'
axis square

Good luck.

[Darwin Tuazon]

Thank you for your response. I compile your code Sulaymon Eshkabilov but there is an error.

>> LORENZ_sys_1ODE

Error: File: LORENZ_sys_1ODE.m Line: 7 Column: 11

Incorrect use of '=' operator. To assign a value to a variable, use '='. To compare values for

equality, use '=='.

Is there anything I did wrong?

Please see your code below.

function df = LORENZ_sys_1ODE(~, x)

% % HELP: Lorenz Functions

% % dx/dt=-sigma*x+sigma*y;

% % dy/dt=- y-x*z;

% % dz/dt=-beta*z+x*y-beta*ro;

sigma=10; beta=8/3; ro=28;

ICs: x(0) =5; y(0) = 5; z(0) = 5; % Your ICs

df=[-sigma*x(1)+sigma*x(2); ...

-x(2)-x(1).*x(3);...

-beta*x(3)+x(1).*x(2)-beta*ro];

ICs=[5, 5, 5]; % Your data

t=[0, 20]; % Your simulation space

OPTs = odeset('reltol', 1e-6, 'abstol', 1e-8); % Optional ODE options set up

[time, fOUT]=ode45(@LORENZ_sys_1ODE, t, ICs, OPTs);

close all

figure

plot3(fOUT(:,1), fOUT(:,2), fOUT(:,3)), grid

xlabel('x(t)'), ylabel('y(t)'), zlabel('z(t)')

title('LORENZ functions x(t) vs. y(t) vs. z(t)')

axis tight

figure

comet3(fOUT(:,1), fOUT(:,2), fOUT(:,3))

figure

subplot(311)

plot(time, fOUT(:,1), 'b','linewidth', 3), grid minor

title 'LORENZ functions x(t), y(t), z(t)', xlabel 'time', ylabel 'x(t)'

subplot(312)

plot( time', fOUT(:,2), 'r', 'linewidth', 2 ), grid minor

xlabel 'time', ylabel 'y(t)'

subplot(313)

plot(time, fOUT(:,3),'k', 'linewidth', 2), grid minor, xlabel 'time', ylabel 'z(t)'

figure

plot(fOUT(:,1), fOUT(:,2), 'b', 'linewidth', 1.5)

grid minor, title('LORENZ functions'), xlabel('x(t)'), ylabel 'y(t)'

axis square

figure

plot(fOUT(:,1), fOUT(:,3), 'k', 'linewidth', 1.5)

grid minor, title('LORENZ functions'), xlabel('x(t)'), ylabel 'z(t)'

axis square

figure

plot(fOUT(:,2), fOUT(:,3), 'm', 'linewidth', 1.5)

grid minor, title('LORENZ functions'), xlabel('y(t)'), ylabel 'z(t)'

axis square

end

Answer 3

[Sulaymon Eshkabilov]

You simulated the code incorrectly. Here is how you should run the code in one m-file:

ICs=[5, 5, 5];  % Your data
t=[0, 20];      % Your simulation space
OPTs = odeset('reltol', 1e-6, 'abstol', 1e-8);  % Optional ODE options set up
[time, fOUT]=ode45(@LORENZ_sys_1ODE, t, ICs, OPTs);
close all 
figure 
plot3(fOUT(:,1), fOUT(:,2), fOUT(:,3)), grid
xlabel('x(t)'), ylabel('y(t)'), zlabel('z(t)')
title('LORENZ functions x(t) vs. y(t) vs. z(t)')
axis tight
figure 
comet3(fOUT(:,1), fOUT(:,2), fOUT(:,3))
figure
subplot(311)
plot(time, fOUT(:,1), 'b','linewidth', 3), grid minor
title 'LORENZ functions x(t), y(t), z(t)', xlabel 'time', ylabel 'x(t)'
subplot(312)
plot( time', fOUT(:,2), 'r', 'linewidth', 2 ), grid minor
xlabel 'time', ylabel 'y(t)'
subplot(313)
plot(time, fOUT(:,3),'k', 'linewidth', 2), grid minor, xlabel 'time', ylabel 'z(t)'

figure
plot(fOUT(:,1), fOUT(:,2), 'b', 'linewidth', 1.5)
grid minor, title('LORENZ functions'), xlabel('x(t)'), ylabel 'y(t)'
axis square

figure
plot(fOUT(:,1), fOUT(:,3), 'k', 'linewidth', 1.5)
grid minor, title('LORENZ functions'), xlabel('x(t)'), ylabel 'z(t)'
axis square

figure
plot(fOUT(:,2), fOUT(:,3), 'm', 'linewidth', 1.5)
grid minor, title('LORENZ functions'), xlabel('y(t)'), ylabel 'z(t)'
axis square

function  df = LORENZ_sys_1ODE(~, x)
% HELP: Lorenz Functions
% dx/dt=-sigma*x+sigma*y;
% dy/dt=- y-x*z;
% dz/dt=-beta*z+x*y-beta*ro;
sigma=10; beta=8/3; ro=28;
% ICs: x(0)=5; y(0)=5; z(0)=5;  % Your ICs
df=[-sigma*x(1)+sigma*x(2); ...
    -x(2)-x(1).*x(3);...
    -beta*x(3)+x(1).*x(2)-beta*ro];
end