[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7137#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7137","headline":"\u30a8\u30ce\u30f3\u5199\u50cf – Wikipedia","name":"\u30a8\u30ce\u30f3\u5199\u50cf – Wikipedia","description":"a = 1.4\u3001b = 0.3\u306e\u30a8\u30ce\u30f3\u5199\u50cf\u306b\u304a\u3051\u308bxn\u3068yn\u306e\u6642\u9593\u767a\u5c55\u3001\u5909\u6570\u306e\u4e0d\u898f\u5247\u306a\u632f\u308b\u821e\u3044\u304c\u898b\u3066\u53d6\u308c\u308b\u3002\u521d\u671f\u5024\uff1ax1=0.1\u3001y1=0\u7e70\u308a\u8fd4\u3057\u6570\uff1an = 500\u307e\u3067 \u30a8\u30ce\u30f3\u5199\u50cf\uff08\u30a8\u30ce\u30f3\u3057\u3083\u305e\u3046\u3001H\u00e9non map\uff09\u3068\u306f\u30012\u6b21\u5143\u306e\u96e2\u6563\u529b\u5b66\u7cfb\u306e\u4e00\u7a2e\u3002\u6b21\u306e2\u5909\u6570\u9023\u7acb\u5e38\u5dee\u5206\u65b9\u7a0b\u5f0f\uff08\u6f38\u5316\u5f0f\uff09\u3067\u793a\u3055\u308c\u308b\u3002 {xn+1=1\u2212axn2+ynyn+1=bxn{displaystyle {begin{cases}x_{n+1}=1-ax_{n}^{2}+y_{n}y_{n+1}=bx_{n}end{cases}}} \u3053\u3053\u3067\u3001a\u3001b\u306f\u5b9a\u6570\u3067\u3001\u5358\u306b\u30d1\u30e9\u30e1\u30fc\u30bf\u306a\u3069\u3068\u547c\u3076\u3002 \u30a8\u30ce\u30f3\u5199\u50cf\u306f\u30011976\u5e74\u306b\u30d5\u30e9\u30f3\u30b9\u306e\u5929\u6587\u5b66\u8005\u30df\u30b7\u30a7\u30eb\u30fb\u30a8\u30ce\u30f3\uff08fr:Michel H\u00e9non\uff09\u306b\u3088\u308a\u767a\u8868\u3055\u308c\u305f\u3002\u30a8\u30ce\u30f3\u306f\u30011963\u5e74\u306b\u767a\u8868\u3055\u308c\u305f\u30ed\u30fc\u30ec\u30f3\u30c4\u65b9\u7a0b\u5f0f\u304c\u751f\u307f\u51fa\u3059\u30ab\u30aa\u30b9\u3092\u3055\u3089\u306b\u7814\u7a76\u3059\u308b\u305f\u3081\u3001\u30ed\u30fc\u30ec\u30f3\u30c4\u306e\u7cfb\u306e\u672c\u8cea\u7684\u6027\u8cea\u3092\u540c\u69d8\u306b\u6301\u3061\u3064\u3064\u3082\u3001\u3088\u308a\u7c21\u5358\u306a\u6570\u5b66\u30e2\u30c7\u30eb\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u306b\u4e0a\u8a18\u306e\u5199\u50cf\u3092\u8003\u6848\u3057\u305f\u3002 \u307e\u305f\u30011969\u5e74\u306b\u30a8\u30ce\u30f3\u304c\u767a\u8868\u3057\u305f\u4ee5\u4e0b\u306e\u5f62\u5f0f\u306e\u5199\u50cf\u306b\u3064\u3044\u3066\u3082\u3001\u3082\u3046\u4e00\u3064\u306e\u30a8\u30ce\u30f3\u5199\u50cf\u3068\u3057\u3066\u7d39\u4ecb\u3055\u308c\u308b\u5834\u5408\u3082\u3042\u308b\u3002 {xn+1=xncos\u2061\u03b1+(yn\u2212xn2)sin\u2061\u03b1yn+1=xnsin\u2061\u03b1+(yn\u2212xn2)cos\u2061\u03b1{displaystyle {begin{cases}x_{n+1}=x_{n}cos alpha +(y_{n}-x_{n}^{2})sin alpha","datePublished":"2022-09-12","dateModified":"2022-09-12","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/4\/42\/X_time_evolution_Henon_map_%28n_from_1_to_100%29.png\/300px-X_time_evolution_Henon_map_%28n_from_1_to_100%29.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/4\/42\/X_time_evolution_Henon_map_%28n_from_1_to_100%29.png\/300px-X_time_evolution_Henon_map_%28n_from_1_to_100%29.png","height":"163","width":"300"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7137","about":["Wikipedia"],"wordCount":1944,"articleBody":"a = 1.4\u3001b = 0.3\u306e\u30a8\u30ce\u30f3\u5199\u50cf\u306b\u304a\u3051\u308bxn\u3068yn\u306e\u6642\u9593\u767a\u5c55\u3001\u5909\u6570\u306e\u4e0d\u898f\u5247\u306a\u632f\u308b\u821e\u3044\u304c\u898b\u3066\u53d6\u308c\u308b\u3002\u521d\u671f\u5024\uff1ax1=0.1\u3001y1=0\u7e70\u308a\u8fd4\u3057\u6570\uff1an = 500\u307e\u3067  \u30a8\u30ce\u30f3\u5199\u50cf\uff08\u30a8\u30ce\u30f3\u3057\u3083\u305e\u3046\u3001H\u00e9non map\uff09\u3068\u306f\u30012\u6b21\u5143\u306e\u96e2\u6563\u529b\u5b66\u7cfb\u306e\u4e00\u7a2e\u3002\u6b21\u306e2\u5909\u6570\u9023\u7acb\u5e38\u5dee\u5206\u65b9\u7a0b\u5f0f\uff08\u6f38\u5316\u5f0f\uff09\u3067\u793a\u3055\u308c\u308b\u3002{xn+1=1\u2212axn2+ynyn+1=bxn{displaystyle {begin{cases}x_{n+1}=1-ax_{n}^{2}+y_{n}y_{n+1}=bx_{n}end{cases}}}\u3053\u3053\u3067\u3001a\u3001b\u306f\u5b9a\u6570\u3067\u3001\u5358\u306b\u30d1\u30e9\u30e1\u30fc\u30bf\u306a\u3069\u3068\u547c\u3076\u3002  \u30a8\u30ce\u30f3\u5199\u50cf\u306f\u30011976\u5e74\u306b\u30d5\u30e9\u30f3\u30b9\u306e\u5929\u6587\u5b66\u8005\u30df\u30b7\u30a7\u30eb\u30fb\u30a8\u30ce\u30f3\uff08fr:Michel H\u00e9non\uff09\u306b\u3088\u308a\u767a\u8868\u3055\u308c\u305f\u3002\u30a8\u30ce\u30f3\u306f\u30011963\u5e74\u306b\u767a\u8868\u3055\u308c\u305f\u30ed\u30fc\u30ec\u30f3\u30c4\u65b9\u7a0b\u5f0f\u304c\u751f\u307f\u51fa\u3059\u30ab\u30aa\u30b9\u3092\u3055\u3089\u306b\u7814\u7a76\u3059\u308b\u305f\u3081\u3001\u30ed\u30fc\u30ec\u30f3\u30c4\u306e\u7cfb\u306e\u672c\u8cea\u7684\u6027\u8cea\u3092\u540c\u69d8\u306b\u6301\u3061\u3064\u3064\u3082\u3001\u3088\u308a\u7c21\u5358\u306a\u6570\u5b66\u30e2\u30c7\u30eb\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u306b\u4e0a\u8a18\u306e\u5199\u50cf\u3092\u8003\u6848\u3057\u305f\u3002\u307e\u305f\u30011969\u5e74\u306b\u30a8\u30ce\u30f3\u304c\u767a\u8868\u3057\u305f\u4ee5\u4e0b\u306e\u5f62\u5f0f\u306e\u5199\u50cf\u306b\u3064\u3044\u3066\u3082\u3001\u3082\u3046\u4e00\u3064\u306e\u30a8\u30ce\u30f3\u5199\u50cf\u3068\u3057\u3066\u7d39\u4ecb\u3055\u308c\u308b\u5834\u5408\u3082\u3042\u308b\u3002{xn+1=xncos\u2061\u03b1+(yn\u2212xn2)sin\u2061\u03b1yn+1=xnsin\u2061\u03b1+(yn\u2212xn2)cos\u2061\u03b1{displaystyle {begin{cases}x_{n+1}=x_{n}cos alpha +(y_{n}-x_{n}^{2})sin alpha y_{n+1}=x_{n}sin alpha +(y_{n}-x_{n}^{2})cos alpha end{cases}}}\u30a8\u30ce\u30f3\u30fb\u30a2\u30c8\u30e9\u30af\u30bf[\u7de8\u96c6]\u30a8\u30ce\u30f3\u5199\u50cf\u306b\u304a\u3051\u308ba\u3001b\u306f\u4efb\u610f\u306e\u5b9a\u6570\u3060\u304c\u3001\u5199\u50cf\u304c\u30b9\u30c8\u30ec\u30f3\u30b8\u30a2\u30c8\u30e9\u30af\u30bf\u3068\u306a\u308b\u3088\u3046\u306a\u6700\u9069\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3057\u3066\u3001\u30a8\u30ce\u30f3\u306fa = 1.4\u3001b = 0.3\u3092\u63d0\u6848\u3057\u3001\u3053\u308c\u3089\u306e\u5024\u304c\u30a8\u30ce\u30f3\u5199\u50cf\u306b\u304a\u3051\u308b\u6a19\u6e96\u7684\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u5024\u3068\u3057\u3066\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u3002\u3053\u306e\u3068\u304d\u306e\u89e3\u8ecc\u9053\u306f\u30a8\u30ec\u30f3\u30fb\u30a2\u30c8\u30e9\u30af\u30bf\u3068\u547c\u3070\u308c\u308b\u3002    \u30a8\u30ce\u30f3\u30fb\u30a2\u30c8\u30e9\u30af\u30bf\u6a2a\u8ef8\uff1axn\u3001\u7e26\u8ef8\uff1ayn\u307e\u305f\u3001\u4ed6\u306e\u30b9\u30c8\u30ec\u30f3\u30b8\u30a2\u30c8\u30e9\u30af\u30bf\u540c\u69d8\u306b\u30a8\u30ec\u30f3\u30fb\u30a2\u30c8\u30e9\u30af\u30bf\u306e\u89e3\u8ecc\u9053\u306f\u30d5\u30e9\u30af\u30bf\u30eb\u69cb\u9020\u3092\u6301\u3064\u3002\u56f3\u5f62\u3092\u62e1\u5927\u3057\u3066\u3044\u304f\u3068\u3001\u7121\u9650\u306b\u76f8\u4f3c\u306e\u5f62\u72b6\u304c\u8868\u308c\u308b\u3002\u30d5\u30e9\u30af\u30bf\u30eb\u6b21\u5143\u306f\u3001\u5bb9\u91cf\u6b21\u5143\uff08\u82f1\u8a9e\u7248\uff09\u3067\u306f\u7d041.27\u3001\u76f8\u95a2\u6b21\u5143\uff08\u82f1\u8a9e\u7248\uff09\u3067\u306f\u7d041.23\u3067\u3042\u308b\u3002  \u30a8\u30ce\u30f3\u30fb\u30a2\u30c8\u30e9\u30af\u30bf\u306e\u30d5\u30e9\u30af\u30bf\u30eb\u69cb\u9020\u7e70\u308a\u8fd4\u3057\u6570\u306f\u3001(1) n = 104\u3001(2) n = 105\u3001(3) n = 106\u3001(4) n = 106(4)\u306f\u62e1\u5927\u7387\u306b\u5bfe\u3057\u3066\u30d7\u30ed\u30c3\u30c8\u6570\uff08\u7e70\u308a\u8fd4\u3057\u6570\uff09\u304c\u5c11\u306a\u3044\u306e\u3067\u3001\u8ecc\u9053\u306e\u70b9\u306b\u9699\u9593\u304c\u76ee\u7acb\u3064\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u5199\u50cf\u306a\u3069\u3068\u540c\u69d8\u306b\u30d1\u30e9\u30e1\u30fc\u30bfa\u3001b\u306e\u5909\u5316\u306b\u5fdc\u3058\u3066\u3001\u30ab\u30aa\u30b9\u3060\u3051\u3067\u306f\u306a\u304f\u3001\u5468\u671f\u7684\u632f\u308b\u821e\u3044\u306b\u843d\u3061\u7740\u3044\u305f\u308a\u3001\u56fa\u5b9a\u70b9\u3078\u53ce\u675f\u3057\u305f\u308a\u3059\u308b\u3088\u3046\u306a\u632f\u308b\u821e\u3044\u306b\u5909\u308f\u308b\u3002\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u5fdc\u3058\u3066\u5199\u50cf\u306e\u5909\u6570\u304c\u6700\u7d42\u7684\u306b\u3069\u306e\u3088\u3046\u306a\u5024\u306b\u843d\u3061\u7740\u304f\u304b\u3092\u793a\u3059\u306e\u306b\u5206\u5c90\u56f3\u304c\u7528\u3044\u3089\u308c\u308b\u304c\u3001\u30a8\u30ce\u30f3\u5199\u50cf\u306e\u3088\u3046\u306a2\u6b21\u5143\u5199\u50cf\u306e\u5834\u5408\u306b\u306f\u3001\u6a2a\u8ef8\u3068\u7e26\u8ef8\u306b\u30d1\u30e9\u30e1\u30fc\u30bf\u5909\u5316\u3092\u53d6\u3063\u3066\u30d1\u30e9\u30e1\u30fc\u30bf2\u3064\u306e\u5909\u5316\u306e\u5f71\u97ff\u3092\u540c\u6642\u306b\u89b3\u5bdf\u3059\u308b2\u30d1\u30e9\u30e1\u30fc\u30bf\u5206\u5c90\u56f3\u3068\u30011\u3064\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u56fa\u5b9a\u3057\u3066\u3082\u30461\u3064\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u5909\u5316\u306e\u5f71\u97ff\u3060\u3051\u3092\u89b3\u5bdf\u3059\u308b1\u30d1\u30e9\u30e1\u30fc\u30bf\u5206\u5c90\u56f3\u304c\u3042\u308b\u3002  \u30a8\u30ce\u30f3\u5199\u50cf\u306e1\u30d1\u30e9\u30e1\u30fc\u30bf\u5206\u5c90\u56f3 b = 0.3\u4e0a\u56f3\u306fb = 0.3\u306b\u304a\u3051\u308b\u30a8\u30ce\u30f3\u5199\u50cf\u306e1\u30d1\u30e9\u30e1\u30fc\u30bf\u5206\u5c90\u56f3\u306e\u4f8b\u3067\u3001\u5404\u7a2e\u306e\u5206\u5c90\u304c\u89b3\u5bdf\u3055\u308c\u308b\u3002a\u304c\u7d040.912\u3092\u8d85\u3048\u308b\u30682\u5468\u671f\u304b\u30894\u5468\u671f\u3078\u306e\u5468\u671f\u500d\u5206\u5c90\u304c\u767a\u751f\u3059\u308b\u3002\u307e\u305f\u3001\u7d041.226\u3092\u8d85\u3048\u308b\u3068\u4e0d\u898f\u5247\u306a\u632f\u308b\u821e\u3044\u304b\u30897\u5468\u671f\u8ecc\u9053\u3078\u5909\u5316\u3059\u308b\u30b5\u30c9\u30eb\u30ce\u30fc\u30c9\u5206\u5c90\u304c\u767a\u751f\u3059\u308b\u3002\u7d041.115\u3068\u7d041.271\u3092\u8d85\u3048\u305f\u3068\u304d\u306b\u306f\u3001\u30a2\u30c8\u30e9\u30af\u30bf\u306e\u8ecc\u9053\u304c\u7a81\u7136\u5927\u304d\u304f\u306a\u308b\u5185\u90e8\u30af\u30e9\u30a4\u30b7\u30b9\u3068\u547c\u3070\u308c\u308b\u73fe\u8c61\u304c\u767a\u751f\u3059\u308b\u3002\u30a8\u30ce\u30f3\u30fb\u30a2\u30c8\u30e9\u30af\u30bf\u306b\u304a\u3051\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u5024\u3067\u3042\u308ba = 1.4\u3092\u8d85\u3048\u3001\u3055\u3089\u306b\u7d041.426\u3092\u8d85\u3048\u308b\u3068\u3001\u30a2\u30c8\u30e9\u30af\u30bf\u3092\u63cf\u3044\u3066\u3044\u305f\u89e3\u8ecc\u9053\u306f\u5d29\u58ca\u3057\u3066\u5909\u6570\u306f\u30de\u30a4\u30ca\u30b9\u3078\u767a\u6563\u3059\u308b\u3088\u3046\u306b\u306a\u308b\u3002\u3053\u308c\u306f\u5883\u754c\u30af\u30e9\u30a4\u30b7\u30b9\u3068\u547c\u3070\u308c\u3001\u672c\u8cea\u7684\u306b\u306f\u5185\u90e8\u30af\u30e9\u30a4\u30b7\u30b9\u3068\u540c\u3058\u73fe\u8c61\u3060\u304c\u30a2\u30c8\u30e9\u30af\u30bf\u8ecc\u9053\u304c\u5927\u304d\u304f\u306a\u308b\u306b\u7559\u307e\u3089\u305a\u3001\u7121\u9650\u9060\u3078\u767a\u6563\u3059\u308b\u3002\u53c2\u8003\u6587\u732e[\u7de8\u96c6]H\u00e9non, Michel (1976). \u201cA two-dimensional mapping with a strange attractor\u201d. Communications in Mathematical Physics (Springer) 50 (1):  69-77. http:\/\/projecteuclid.org\/euclid.cmp\/1103900150.\u00a0H\u00e9non, Michel (October 1969). \u201cNumerical Study of Quadratic Area-Preserving Mappings\u201d. Quarterly of Applied Mathematics (Brown University) 27 (3):  291-312.\u00a0\u5c0f\u5ba4\u5143\u653f\u30012005\u3001\u300e\u57fa\u790e\u304b\u3089\u306e\u529b\u5b66\u7cfb -\u5206\u5c90\u89e3\u6790\u304b\u3089\u30ab\u30aa\u30b9\u7684\u904d\u6b74\u3078-\u300f\u65b0\u7248\u3001\u30b5\u30a4\u30a8\u30f3\u30b9\u793e\u00a0ISBN\u00a04-7819-1118-8\u5408\u539f\u4e00\u5e78\u30fb\u9ed2\u5d0e\u653f\u7537\u30fb\u9ad8\u6a4b\u7d14\u3001\u9060\u85e4\u8aed\uff08\u7de8\uff09\u30011999\u3001\u300e\u54f2\u5b66\u8005\u30af\u30ed\u30b5\u30ad\u3068\u5de5\u5b66\u8005\u30a2\u30a4\u30cf\u30e9\u306e\u795e\u306f\u30ab\u30aa\u30b9\u306b\u5bbf\u308a\u305f\u3082\u3046\u300f\u521d\u7248\u3001\u30a2\u30b9\u30ad\u30fc\u00a0ISBN\u00a04-7561-3133-6K.T.\u30a2\u30ea\u30b0\u30c3\u30c9\u30fbT.D.\u30b5\u30a6\u30a2\u30fc\u30fbJ.A.\u30e8\u30fc\u30af\u3001\u30b7\u30e5\u30d7\u30ea\u30f3\u30ac\u30fc\u30fb\u30b8\u30e3\u30d1\u30f3\uff08\u7de8\uff09\u3001\u6d25\u7530\u4e00\u90ce\uff08\u76e3\u8a33\uff09\u3001\u661f\u91ce\u9ad8\u5fd7\u30fb\u963f\u90e8\u5de8\u4ec1\u30fb\u9ed2\u7530\u62d3\u30fb\u677e\u672c\u548c\u5b8f\uff08\u8a33\uff09\u30012012\u3001\u300e\u30ab\u30aa\u30b9\u3000\u7b2c1\u5dfb\u3000\u529b\u5b66\u7cfb\u5165\u9580\u300f\u3001\u4e38\u5584\u51fa\u7248\u00a0ISBN\u00a0978-4-621-06223-4Eric W. Weisstein. \u201cH\u00e9non Map\u201d. MathWorld.   Wolfram Research. 2014\u5e7410\u670826\u65e5\u95b2\u89a7\u3002"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7137#breadcrumbitem","name":"\u30a8\u30ce\u30f3\u5199\u50cf – Wikipedia"}}]}]