Simulating the Logistic Map in Matlab

This video shows how simple it is to simulate discrete-time dynamical systems, such as the Logistic Map, in Matlab.

This video was produced at the University of Washington

[Downloader]

One of the best tutorials I have ever seen. Thank you.

[harmony]

Smart way to store steady state Thankyou very much sir. I'm trying it right now.

[duongn.t]

Thanks!! Really helpful for my thesis.

[shkhrvarshney]

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.

[loveat]

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 r<-2 and r>4. Thank you for sharing!!

[fvcfvc-yf]

Many thanks, very clear explanation :D

[Leodecryptoboss]

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.

[mselmanerel]

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;

[amanthakur]

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

[lumpi]

Thank you for this video ! But I don't understand why there are 2 loops for the computing of x(k)...

[NormanLim]

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?

[coenpelsrijcken]

is there a reason for the first imbedded for loop?

[baonguyenhoang]

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.

[christinearrellin]

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.

[housamkak]

are you using schemer for dark theme or something else?

[TheQwampa]

Is there a way to extend this diagram beyond r=4? Seems like it goes to negative infinity after that.

[jasimuddin]

Do you have any video about Maximum Lyapunov Exponent? If you have give the link. Thank you.

[hms]

What is the purpose of code lines 8 to 12?

[Goakshay]

Can you please share m.file of Lorenz attractor bifurcation plot...

[tanveerulhaq]

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



end

Kindly help me for this. I am using this in my research work. I will be than full to you.