- Computation Of The Feigenbaum Delta Compute The Feigenbaum Delta From The Logistic Map The Logistic Map Is Given By X 1 (69.9 KiB) Viewed 22 times
- Computation Of The Feigenbaum Delta Compute The Feigenbaum Delta From The Logistic Map The Logistic Map Is Given By X 2 (16.15 KiB) Viewed 22 times
Computation of the Feigenbaum delta Compute the Feigenbaum delta from the logistic map. The logistic map is given by X₁+1 = μx; (1-x₂), and the Feigenbaum delta is defined as 8 = lim 8, where Sn n→∞ = mn-1 - mn-2 mn-mn-1 and where m, is the value of μ 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 m, using mn-1, mn-2 and §n-1. 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 Computex and x' Loop 3 (end) One step of Newton's method Loop 2 (end) Save m, and compute 8, Loop 1 (end) Grading will be done on the converged values of 6, up to n = 11. Set &₁ = 5.
clc; clear all; start_time=clock; a0=2; a1=1;1+sqrt(5);d=4 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 end = end res=a*res*(1-res); a=a-(res-0.5)/der; d=(vpa(a1)-vpa(aº))/(vpa(a)-vpa(al)); fprintf('Approximation number%2g %18.15f\n',k, double (d)); a0=al; al-a; end end_time=clock; total_time=end_time-start_time;
d = 4 Approximation number 3 0.000000000000000 Error using / Division by zero. Error in solution (line 13) a=a1 + (a1-a0)/(d);