How can I use Lorenz Attractor code?
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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.
2 Comments
KALYAN ACHARJYA
on 25 May 2019
Edited: KALYAN ACHARJYA
on 25 May 2019
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
Answers (3)
Sulaymon Eshkabilov
on 26 May 2019
Edited: Sulaymon Eshkabilov
on 26 May 2019
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.
3 Comments
Ghofran Khaled
on 15 Nov 2021
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
Sulaymon Eshkabilov
on 26 May 2019
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.
Sulaymon Eshkabilov
on 14 Nov 2021
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
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