【求助】求feigenbaum常数的MATLAB计算程序
请问哪位大哥有feigenbaum常数计算的MATLAB程序，有的能否传一份给小弟，谢谢啦，我的邮箱：haiming9060@126.com[ 本帖最后由 海上飞鱼 于 2010-6-14 23:17 编辑 ] feigenbaum常数的计算，是很麻烦的。根据郑伟谋、郝柏林《实用符号动力学》一书，feigenbaum常数的精确值，是采取逼近方法计算的。即先要将各个倍周期分岔点算出来，然后计算相邻分岔点差的绝对值的商a；当计算到n=2^20分岔时，a就非常接近feigenbaum常数了。
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嗯，但是计算各分岔点就非常困难！况且编程不好编！ 的确是不好计算分岔值~~网上搜程序搜不到啊{:{09}:}{:{09}:} 下面的程序应该可以参考一下function feigenbaum
% feigenbaum.m
% Jeremie Korta
% December 1, 2003
% The following program will compute the Feigenbaum ratio using parameter
% values r(n) at superstable fixed points of f^(2^n).As a check, the
% program can be used to estimate the same ratio using period doubling
% cascade from 3-cycle, which is superstable at r = 1.7549... taking the
% unimodular map to be r-x^2.
clear n r R c;
global n q c
max=10;
q = 2; % if you want to find the Feigenbaum ratio for higher order maxima
% change this parameter (the 3-cycle will no longer be stable at the same r!)
% Known superstable r for 1 and 2-cycles for any q.
c = 0; % signifies we're searching from 2-cycle
r(1)=0; % for 1-cycle to be superstable, r = 0
r(2)=1;% for 2-cycle, r = 1.
% We can also calculate the Feigenbaum ratio at the 3-cycle
% period-doubling cascade (for q=2).Hopefully, it's still 4.6692... !
%c = 1; % signifies we're searching from 3-cycle
%r(1) = 1.7549;% superstable 3-cycle occurs at r = 1.7549...
for i=2:max
n=i-1;
del=10^(-n-c); % smaller for 3-cycle window
next=r(i-1)+del;
prev_sign=sign(func(next));
while (sign(func(next))==prev_sign)
next=next+del;
end
r(i)=fzero(@func, );
end
for j=1:(max-2)
R(j)=(r(j)-r(j+1))/(r(j+1)-r(j+2));
end
fprintf('\n Best estimate of Feigenbaum ratio = %1.6f', R(max-2))
% File: func.m
%
% func returns the f^(2^n) map of 0 where f = r-x^(2q) q=1,2,3... if
% c = 0, or the f^(3*2^n) map of 0 if c = 1.The zero of this function
% occurs at the superstable value r(n).
function x=func(r)
global n q c
x=0;
for i=1:((c > 0)*2+1)*2^n
x = r - x^q;
end
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