{"id":113,"date":"2011-04-13T01:46:00","date_gmt":"2011-04-13T01:46:00","guid":{"rendered":"http:\/\/witpoko.com\/?p=113"},"modified":"2011-04-13T01:46:00","modified_gmt":"2011-04-13T01:46:00","slug":"%e0%b8%aa%e0%b8%a3%e0%b9%89%e0%b8%b2%e0%b8%87-bifurcation-diagram-%e0%b9%81%e0%b8%9a%e0%b8%9a%e0%b8%87%e0%b9%88%e0%b8%b2%e0%b8%a2%e0%b9%86","status":"publish","type":"post","link":"https:\/\/witpoko.com\/?p=113","title":{"rendered":"\u0e2a\u0e23\u0e49\u0e32\u0e07 Bifurcation Diagram \u0e41\u0e1a\u0e1a\u0e07\u0e48\u0e32\u0e22\u0e46"},"content":{"rendered":"<p><a href=\"https:\/\/i0.wp.com\/2.bp.blogspot.com\/-nyC3TFPVGUw\/TaUDNLk6bwI\/AAAAAAAAF3c\/LR2qh1Yf_HY\/s1600\/bifurcation.png\"><img data-recalc-dims=\"1\" decoding=\"async\" style=\"display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 251px;\" src=\"https:\/\/i0.wp.com\/2.bp.blogspot.com\/-nyC3TFPVGUw\/TaUDNLk6bwI\/AAAAAAAAF3c\/LR2qh1Yf_HY\/s400\/bifurcation.png\" border=\"0\" alt=\"\" id=\"BLOGGER_PHOTO_ID_5594881637058506498\" \/><\/a><br \/>\u0e1e\u0e2d\u0e14\u0e35\u0e21\u0e35\u0e19\u0e31\u0e01\u0e40\u0e23\u0e35\u0e22\u0e19\u0e15\u0e31\u0e49\u0e07\u0e01\u0e23\u0e30\u0e17\u0e39\u0e49\u0e16\u0e32\u0e21\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e07\u0e01\u0e32\u0e23\u0e27\u0e32\u0e14\u0e23\u0e39\u0e1b\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e07 <a href=\"http:\/\/en.wikipedia.org\/wiki\/Bifurcation_diagram\">Bifurcation Diagram<\/a> \u0e40\u0e21\u0e37\u0e48\u0e2d\u0e04\u0e37\u0e19 \u0e1c\u0e21\u0e40\u0e25\u0e22\u0e17\u0e14\u0e25\u0e2d\u0e07\u0e27\u0e32\u0e14\u0e1a\u0e19 <i>Mathematica<\/i> \u0e40\u0e2b\u0e47\u0e19\u0e27\u0e48\u0e32\u0e27\u0e34\u0e18\u0e35\u0e27\u0e32\u0e14\u0e07\u0e48\u0e32\u0e22\u0e14\u0e35 \u0e40\u0e25\u0e22\u0e21\u0e32\u0e1a\u0e31\u0e19\u0e17\u0e36\u0e01\u0e44\u0e27\u0e49\u0e40\u0e1c\u0e37\u0e48\u0e2d\u0e21\u0e35\u0e43\u0e04\u0e23\u0e04\u0e49\u0e19\u0e2b\u0e32\u0e2d\u0e35\u0e01\u0e43\u0e19\u0e2d\u0e19\u0e32\u0e04\u0e15 \u0e16\u0e49\u0e32\u0e08\u0e30\u0e25\u0e2d\u0e07\u0e01\u0e47\u0e04\u0e31\u0e14\u0e25\u0e2d\u0e01\u0e40\u0e2d\u0e32\u0e44\u0e1b\u0e25\u0e2d\u0e07\u0e44\u0e14\u0e49\u0e40\u0e25\u0e22 \u0e41\u0e25\u0e49\u0e27\u0e40\u0e1b\u0e25\u0e35\u0e48\u0e22\u0e19\u0e19\u0e39\u0e48\u0e19\u0e40\u0e1b\u0e25\u0e35\u0e48\u0e22\u0e19\u0e19\u0e35\u0e48\u0e40\u0e25\u0e48\u0e19\u0e14\u0e39\u0e40\u0e2d\u0e07<\/p>\n<div><\/p>\n<div><i><br \/><\/i><\/div>\n<div>\n<div><i>(* \u0e01\u0e33\u0e2b\u0e19\u0e14 mapping \u0e17\u0e35\u0e48\u0e40\u0e23\u0e32\u0e2a\u0e19\u0e43\u0e08 \u0e2d\u0e31\u0e19\u0e19\u0e35\u0e49\u0e40\u0e23\u0e35\u0e22\u0e01\u0e27\u0e48\u0e32 logistic map *)<\/i><\/div>\n<div><i>f[r_, x_] := r x (1 &#8211; x)<\/i><\/div>\n<div><i><br \/><\/i><\/div>\n<div><i>(* \u0e17\u0e33\u0e01\u0e32\u0e23 iterate \u0e14\u0e49\u0e27\u0e22 &#8216;r&#8217; \u0e44\u0e1b &#8216;iterations&#8217; \u0e04\u0e23\u0e31\u0e49\u0e07 \u0e40\u0e23\u0e34\u0e48\u0e21\u0e14\u0e49\u0e27\u0e22 &#8216;x0&#8217; \u0e41\u0e25\u0e49\u0e27\u0e15\u0e31\u0e14\u0e21\u0e32\u0e14\u0e39 &#8216;count&#8217; \u0e15\u0e31\u0e27 *)<\/i><\/div>\n<div><i>longtermValues[r_, count_, iterations_, x0_] := <\/i><\/div>\n<div><i> Map[{r, #} &amp;, Take[NestList[f[r, #] &amp;, x0, iterations], -count]]  <\/i><\/div>\n<div><i><br \/><\/i><\/div>\n<div><i>(* \u0e40\u0e23\u0e32\u0e40\u0e1b\u0e25\u0e35\u0e48\u0e22\u0e19 r \u0e15\u0e31\u0e49\u0e07\u0e41\u0e15\u0e48 2.6 \u0e44\u0e1b\u0e08\u0e19\u0e16\u0e36\u0e07 4 \u0e42\u0e14\u0e22\u0e02\u0e22\u0e31\u0e1a\u0e17\u0e35\u0e25\u0e30 0.001 \u0e2a\u0e33\u0e2b\u0e23\u0e31\u0e1a\u0e41\u0e15\u0e48\u0e25\u0e30 r \u0e40\u0e23\u0e32 iterate 500 \u0e04\u0e23\u0e31\u0e49\u0e07\u0e41\u0e25\u0e49\u0e27\u0e40\u0e2d\u0e32 200 \u0e15\u0e31\u0e27\u0e2a\u0e38\u0e14\u0e17\u0e49\u0e48\u0e32\u0e22<\/i><i>\u0e21\u0e32\u0e43\u0e0a\u0e49 <\/i><i> \u0e40\u0e23\u0e32\u0e15\u0e49\u0e2d\u0e07\u0e43\u0e0a\u0e49 Flatten[&#8230;,1] \u0e40\u0e1e\u0e37\u0e48\u0e2d\u0e43\u0e2b\u0e49\u0e04\u0e39\u0e48\u0e25\u0e33\u0e14\u0e31\u0e1a\u0e17\u0e31\u0e49\u0e07\u0e2b\u0e21\u0e14\u0e2d\u0e22\u0e39\u0e48\u0e43\u0e19\u0e25\u0e34\u0e2a\u0e17\u0e4c\u0e23\u0e30\u0e14\u0e31\u0e1a\u0e40\u0e14\u0e35\u0e22\u0e27\u0e01\u0e31\u0e19 *)<\/i><\/div>\n<div><i>allValues = Flatten[Table[longtermValues[r, 200, 500, 0.2], {r, 2.6, 4, 0.001}], 1];<\/i><\/div>\n<div><i><br \/><\/i><\/div>\n<div><i>(* \u0e27\u0e32\u0e14\u0e23\u0e39\u0e1b *)<\/i><\/div>\n<div><i>ListPlot[allValues, PlotStyle -&gt; PointSize[0.001]]<\/i><\/div>\n<div><\/div>\n<div><\/div>\n<div><\/div>\n<div><\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0e1e\u0e2d\u0e14\u0e35\u0e21\u0e35\u0e19\u0e31\u0e01\u0e40\u0e23\u0e35\u0e22\u0e19\u0e15\u0e31\u0e49\u0e07\u0e01\u0e23\u0e30\u0e17\u0e39\u0e49\u0e16\u0e32\u0e21\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e07\u0e01\u0e32\u0e23\u0e27\u0e32\u0e14\u0e23\u0e39\u0e1b\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e07 Bifurcation Diagram \u0e40\u0e21\u0e37\u0e48\u0e2d\u0e04\u0e37\u0e19 \u0e1c\u0e21\u0e40\u0e25\u0e22\u0e17\u0e14\u0e25\u0e2d\u0e07\u0e27\u0e32\u0e14\u0e1a\u0e19 Mathematica \u0e40\u0e2b\u0e47\u0e19\u0e27\u0e48\u0e32\u0e27\u0e34\u0e18\u0e35\u0e27\u0e32\u0e14\u0e07\u0e48\u0e32\u0e22\u0e14\u0e35 \u0e40\u0e25\u0e22\u0e21\u0e32\u0e1a\u0e31\u0e19\u0e17\u0e36\u0e01\u0e44\u0e27\u0e49\u0e40\u0e1c\u0e37\u0e48\u0e2d\u0e21\u0e35\u0e43\u0e04\u0e23\u0e04\u0e49\u0e19\u0e2b\u0e32\u0e2d\u0e35\u0e01\u0e43\u0e19\u0e2d\u0e19\u0e32\u0e04\u0e15 \u0e16\u0e49\u0e32\u0e08\u0e30\u0e25\u0e2d\u0e07\u0e01\u0e47\u0e04\u0e31\u0e14\u0e25\u0e2d\u0e01\u0e40\u0e2d\u0e32\u0e44\u0e1b\u0e25\u0e2d\u0e07\u0e44\u0e14\u0e49\u0e40\u0e25\u0e22 \u0e41\u0e25\u0e49\u0e27\u0e40\u0e1b\u0e25\u0e35\u0e48\u0e22\u0e19\u0e19\u0e39\u0e48\u0e19\u0e40\u0e1b\u0e25\u0e35\u0e48\u0e22\u0e19\u0e19\u0e35\u0e48\u0e40\u0e25\u0e48\u0e19\u0e14\u0e39\u0e40\u0e2d\u0e07 (* \u0e01\u0e33\u0e2b\u0e19\u0e14 mapping \u0e17\u0e35\u0e48\u0e40\u0e23\u0e32\u0e2a\u0e19\u0e43\u0e08 \u0e2d\u0e31\u0e19\u0e19\u0e35\u0e49\u0e40\u0e23\u0e35\u0e22\u0e01\u0e27\u0e48\u0e32 logistic &hellip; <a title=\"\u0e2a\u0e23\u0e49\u0e32\u0e07 Bifurcation Diagram \u0e41\u0e1a\u0e1a\u0e07\u0e48\u0e32\u0e22\u0e46\" class=\"hm-read-more\" href=\"https:\/\/witpoko.com\/?p=113\"><span class=\"screen-reader-text\">\u0e2a\u0e23\u0e49\u0e32\u0e07 Bifurcation Diagram \u0e41\u0e1a\u0e1a\u0e07\u0e48\u0e32\u0e22\u0e46<\/span>Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[2,31,108,29,100,4],"tags":[],"class_list":["post-113","post","type-post","status-publish","format-standard","hentry","category-education","category-math","category-math-geek","category-mathematica","category-physics","category-4"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p4UNq0-1P","_links":{"self":[{"href":"https:\/\/witpoko.com\/index.php?rest_route=\/wp\/v2\/posts\/113","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/witpoko.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/witpoko.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/witpoko.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/witpoko.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=113"}],"version-history":[{"count":0,"href":"https:\/\/witpoko.com\/index.php?rest_route=\/wp\/v2\/posts\/113\/revisions"}],"wp:attachment":[{"href":"https:\/\/witpoko.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=113"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/witpoko.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=113"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/witpoko.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}