Hello. Feigenbaum delta from the logistic map. Been stuck for hours and i dont know how to solve it. Please tell me my mistake and if its completly wrong please tell me

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food lover 2024-1-17

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https://ww2.mathworks.cn/matlabcentral/answers/2071121-hello-feigenbaum-delta-from-the-logistic-map-been-stuck-for-hours-and-i-dont-know-how-to-solve-it

评论： food lover 2024-1-22

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THE QUESTION

Compute the Feigenbaum delta from the logistic map. The logistic map is given by

,

and the Feigenbaum delta is defined as

where

and where

is the value of μ for which

is in the orbit of the period-N cycle with

.

Here is a resonable outline:

Loop 1 Start at period-

with

, and increment n with each iteration

Compute initial guess for

using

,

and

.

Loop 2 Iterate Newton's method, either a fixed number of times or until convergence

Initialize logistic map

Loop 3 Iterate the logistic map

times

Compute x and

Loop 3 (end)

One step of Newton's method

Loop 2 (end)

Save

and compute

Loop 1 (end)

Grading will be done on the converged values of

up to

. Set

.

 clc
 clear all;
 start_time = clock;
 a0 = 2; a1 = 1+ sqrt(5); d=4;
 mu(1)=a0;
 mu(2)=a1;
 for k = 3:15
     a = a1 + (al-a0)/d;
     
     
 for i = 1:2
     res = 0.5; der = 0;
     for j = 2:2^(k-1)+1
         der = res*(1-res)+ a*(1-2*res)*der;
     end
     
     a= a-(res-0.5)/der;
 end
 
 %d = (a1-a0)/(a-a1); % approxima
              fins a 4.66919841237705
             
 d = (vpa(a1)-vpa(a0))/(vpa(a)-vpa(a1));
              % approxima a 4.69201587522386
              
              que, s clarament
   millor
   fprintf('Approximaci n mero % us %.15f/n', k,double(d));
          a0 = a1,
          a1 = a;
          
          mu(k)=a;
 end
 end_time= clock;
 total_time= end_time-start_time

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Dyuman Joshi 2024-1-22

What is the expected output from the question?

Is it a script-based problem or a function-based problem?

Also, some pointers for the code -

> You don't need to use vpa() here, so remove it.

> tic-toc will be a better fit here instead of clock

However, is it necessary to calculate the time taken by the code in the question?

food lover 2024-1-22

Feigenbaum delta = 4.669201609102047

script based

and yes i believe so

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Answer 1

Vinayak 2024-1-19

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https://ww2.mathworks.cn/matlabcentral/answers/2071121-hello-feigenbaum-delta-from-the-logistic-map-been-stuck-for-hours-and-i-dont-know-how-to-solve-it#answer_1393201

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Hi,

After analysing your code and the required map, I found a few issues. It is my understanding that you are referring to variable ‘a1’ instead of ‘al’ inside the for loop. I have modified the calculation of “d” according to the equation shared. Here is the updated code:

clc 
clear all; 
start_time = clock; 
a0 = 2; a1 = 1 + sqrt(5); d = 4; 
mu = zeros(1, 15);  % Initialize mu array 
mu(1) = a0; 
mu(2) = a1; 
for k = 3:15 
    a = a1 + (a1 - a0) / d; 
    for i = 1:2 
        res = 0.5; der = 0; 
        for j = 2:2^(k - 1) + 1 
            der = res * (1 - res) + a * (1 - 2 * res) * der; 
        end 
        a = a - (res - 0.5) / der; 
    end 
    
    % Corrected indexing for mu array 
    d = (mu(k-1) - mu(k-2)) / (mu(k) - mu(k-1)); 
    fprintf('Approximation number %d is %.15f\n', k, double(d)); 
    
    a0 = a1; 
    a1 = a; 
    mu(k) = a; 
end 
end_time = clock; 
total_time = etime(end_time, start_time); 
fprintf('Total time: %f seconds\n', total_time); 

The above updated code correctly computes the Feigenbaum delta from the logistic map.

Hope this helps!

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Dyuman Joshi 2024-1-22

@food lover, There is no "num_doublings" parameter in the answer above, nor is there a for loop with n as the loop index.

So the error does not stem from the code given by @Vinayak.

Unless we know what code you have provided as the solution and what exactly is the question asking, it is difficult to provide any suggestions.

food lover 2024-1-22

i just inserted his work onto mathlab.

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Hello. Feigenbaum delta from the logistic map. Been stuck for hours and i dont know how to solve it. Please tell me my mistake and if its completly wrong please tell me

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Hello. Feigenbaum delta from the logistic map. Been stuck for hours and i dont know how to solve it. Please tell me my mistake and if its completly wrong please tell me

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