Computation Of The Feigenbaum Delta Compute The Feigenbaum Delta From The Logistic Map The Logistic Map Is Given By X 1 1 (59.74 KiB) Viewed 63 times
Computation Of The Feigenbaum Delta Compute The Feigenbaum Delta From The Logistic Map The Logistic Map Is Given By X 1 2 (30.8 KiB) Viewed 63 times
Computation of the Feigenbaum delta Compute the Feigenbaum delta from the logistic map. The logistic map is given by X+1 = px (1 - x0). and the Feigenbaum delta is defined as M-1-M-2 8 = lim 8, where 8, mm-1 and where m, is the value of x for which xo = 1/2 is in the orbit of the period- N cycle with N = 2". Here is a resonable outline: Loop 1 Start at period-2" with n=2, and increment n with each iteration Compute initial guess for using my-2 and 8-13 Loop 2 Iterate Newton's method, either a fixed number of times or until convergence Initialize logistic map Loop 3 Iterate the logistic map 2 times Computer and Loop 3 (end) One step of Newton's method Loop 2 (end) Save m, and computer Loop 1 (end) Grading will be done on the converged values of up to n=11. Set 6 = 5.
made Script B Save C 1 % Compute the Feigenbaum delta 2 % Store approximate values in the row vector delta for assessment, where length(delta)- num_doublings and 3 % delta(2:num doublings) are computed from the algorithm described in Lectures 21-23. 4 num doublings-11; delta zeros(1, num doublings); delta(1)-5; 5 % write your code here 6 7 1 B 9 10 11 12 12 14 15 16 17 % Output your results 18 fprintf('n delta(n)\n'); 19 for n=1. num doublings 20 fprintf("28 %18.15F\n', n, delta(n)); 21 end 22
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