I set up my code so I could also look at -r values and the results are interesting. The doubling period begins at Xss = 0 for -r values rather than Xss = 0.6 for +r values. Things seem to go to infinity r4. Thank you for sharing!!
Thank you, Professor! Even though the the aim of the video to explain how to code the map, you could also point out the Feigenbaum constant after plotting.
Sir once we convert the koopman model to bilinear form then how can we confirm that we had done right conversion from state space to bilinear using Koopman canonical transformation
Matlab Code below is more understandable for this video. In the code, I just obtained steady-state portion. X matrice is composed of Nn rows samples and Nr rows for bifurcation parameters. Matlab Code: n = linspace(1,100); Nn = length(n); r = 0:0.005:4; Nr = length(r); x = zeros(Nn,Nr); x(1,:) = 0.5; count = 0; for r = 0:0.005:4.0-0.005 for n = 1:Nn-1 x(n+1,count+1) = r*x(n,count+1)*(1 - x(n,count+1)); end plot(r*ones(31,1),x(70:Nn,count+1), '.', 'markersize', 2); hold on; count = count+1; end title('Bifurcation diagram of the logistic map'); xlabel('r'); ylabel('x_n'); set(gca, 'xlim', [0 4.0]); hold off;
Hi thank you for your useful video. I'm starting to learn Programming. I have a doubt about ''.. cut out transient.. for i=1:2000...'' I'm not actually understand how it work. Any suggestions appreciated.
Hard to follow along with his screen. When I tried on my end, I got "invalid espression." Obviously I need to input more information but it has been so long that I worked with MATLAB that I have forgotten how to use this program.
how to calculate the lyapunov exponent for 3 or 4 dimensions. for example: x(1) = 0.8109; y(1) = 0.3342; z(1) = 0.5734; lamda = 3.789; beta = 0.029;alpha = 0.0224; for i = 1:2000 x(i+1)=lamda*x(i)*(1-x(i))+beta*((y(i)).^2)*x(i)+alpha*((z(i)).^3); y(i+1)=lamda*y(i)*(1-y(i))+beta*((z(i)).^2)*y(i)+alpha*((x(i)).^3); z(i+1)=lamda*z(i)*(1-z(i))+beta*((z(i)).^2)*z(i)+alpha*((y(i)).^3); end Kindly help me for this. I am using this in my research work. I will be than full to you.
One of the best tutorials I have ever seen. Thank you.
Smart way to store steady state Thankyou very much sir. I'm trying it right now.
Thanks!
I set up my code so I could also look at -r values and the results are interesting. The doubling period begins at Xss = 0 for -r values rather than Xss = 0.6 for +r values. Things seem to go to infinity r4. Thank you for sharing!!
is there a reason for the first imbedded for loop?
Thanks!! Really helpful for my thesis.
Thank you, Professor!
Even though the the aim of the video to explain how to code the map, you could also point out the Feigenbaum constant after plotting.
Thank you for this video ! But I don't understand why there are 2 loops for the computing of x(k)...
Sir once we convert the koopman model to bilinear form then how can we confirm that we had done right conversion from state space to bilinear using Koopman canonical transformation
Many thanks, very clear explanation :D
Matlab Code below is more understandable for this video. In the code, I just obtained steady-state portion. X matrice is composed of Nn rows samples and Nr rows for bifurcation parameters.
Matlab Code:
n = linspace(1,100);
Nn = length(n);
r = 0:0.005:4;
Nr = length(r);
x = zeros(Nn,Nr);
x(1,:) = 0.5;
count = 0;
for r = 0:0.005:4.0-0.005
for n = 1:Nn-1
x(n+1,count+1) = r*x(n,count+1)*(1 - x(n,count+1));
end
plot(r*ones(31,1),x(70:Nn,count+1), '.', 'markersize', 2);
hold on;
count = count+1;
end
title('Bifurcation diagram of the logistic map');
xlabel('r'); ylabel('x_n');
set(gca, 'xlim', [0 4.0]);
hold off;
Aside from the lessons, I also want to learn how the video was done --- I mean how could he project the image on his laptop onto the glass blackboard?
Hi thank you for your useful video. I'm starting to learn Programming.
I have a doubt about ''.. cut out transient.. for i=1:2000...'' I'm not actually understand how it work.
Any suggestions appreciated.
now I understand, thank you so much
Excellent video, thankyou!
You are outstanding
Do you have any video about Maximum Lyapunov Exponent? If you have give the link. Thank you.
Hard to follow along with his screen. When I tried on my end, I got "invalid espression." Obviously I need to input more information but it has been so long that I worked with MATLAB that I have forgotten how to use this program.
Great video Steve. I would be glad if you could do a video on how to reduce 3D system using center manifold with Matlab or Mathematica.
You are God among humans
ha ha nice one
Awsome video, very helpful.
What is the purpose of code lines 8 to 12?
are you using schemer for dark theme or something else?
Is there a way to extend this diagram beyond r=4? Seems like it goes to negative infinity after that.
What an awesome video
Can you please share m.file of Lorenz attractor bifurcation plot...
What a great video, thanks!
well, this is super cool!
Thanks!
how to calculate the lyapunov exponent for 3 or 4 dimensions. for example:
x(1) = 0.8109; y(1) = 0.3342; z(1) = 0.5734;
lamda = 3.789; beta = 0.029;alpha = 0.0224;
for i = 1:2000
x(i+1)=lamda*x(i)*(1-x(i))+beta*((y(i)).^2)*x(i)+alpha*((z(i)).^3);
y(i+1)=lamda*y(i)*(1-y(i))+beta*((z(i)).^2)*y(i)+alpha*((x(i)).^3);
z(i+1)=lamda*z(i)*(1-z(i))+beta*((z(i)).^2)*z(i)+alpha*((y(i)).^3);
end
Kindly help me for this. I am using this in my research work. I will be than full to you.
great
love it