【求助】求feigenbaum常数的MATLAB计算程序

海上飞鱼

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 ]

tangyz_hust

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。

海上飞鱼

嗯，但是计算各分岔点就非常困难！况且编程不好编！

yoonssica

的确是不好计算分岔值~~网上搜程序搜不到啊

gghhjj

下面的程序应该可以参考一下

1. function feigenbaum
   
2. % feigenbaum.m
   
3. % Jeremie Korta
   
4. % December 1, 2003
   
5. % The following program will compute the Feigenbaum ratio using parameter
   
6. % values r(n) at superstable fixed points of f^(2^n).  As a check, the
   
7. % program can be used to estimate the same ratio using period doubling
   
8. % cascade from 3-cycle, which is superstable at r = 1.7549... taking the
   
9. % unimodular map to be r-x^2.
   
10. 
    
11. clear n r R c;
    
12. global n q c
    
13. 
    
14. max=10;   
    
15. q = 2; % if you want to find the Feigenbaum ratio for higher order maxima
    
16. % change this parameter (the 3-cycle will no longer be stable at the same r!)
    
17. 
    
18. % Known superstable r for 1 and 2-cycles for any q.
    
19. c = 0; % signifies we're searching from 2-cycle
    
20. r(1)=0;   % for 1-cycle to be superstable, r = 0
    
21. r(2)=1;  % for 2-cycle, r = 1.
    
22. 
    
23. % We can also calculate the Feigenbaum ratio at the 3-cycle
    
24. % period-doubling cascade (for q=2).  Hopefully, it's still 4.6692... !
    
25. %c = 1; % signifies we're searching from 3-cycle
    
26. %r(1) = 1.7549;  % superstable 3-cycle occurs at r = 1.7549...
    
27.          
    
28. for i=2:max
    
29.     n=i-1;
    
30.     del=10^(-n-c); % smaller for 3-cycle window
    
31.     next=r(i-1)+del;
    
32.     prev_sign=sign(func(next));
    
33.     while (sign(func(next))==prev_sign)
    
34.        next=next+del;
    
35.     end
    
36. 
    
37.     r(i)=fzero(@func, [r(i-1)+10^(-n-1-c), next]);
    
38. 
    
39. end
    
40. 
    
41. for j=1:(max-2)
    
42.     R(j)=(r(j)-r(j+1))/(r(j+1)-r(j+2));
    
43. end
    
44. 
    
45. fprintf('\n Best estimate of Feigenbaum ratio = %1.6f', R(max-2))
    
46. 
    
47. 
    
48. 
    
49. 
    
50. % File: func.m
    
51. %
    
52. % func returns the f^(2^n) map of 0 where f = r-x^(2q) q=1,2,3... if
    
53. % c = 0, or the f^(3*2^n) map of 0 if c = 1.  The zero of this function
    
54. % occurs at the superstable value r(n).
    
55. 
    
56. function x=func(r)
    
57.    
    
58. global n q c
    
59. x=0;
    
60. for i=1:((c > 0)*2+1)*2^n
    
61.     x = r - x^q;
    
62. end

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