{"id":662,"date":"2026-01-04T23:14:33","date_gmt":"2026-01-04T14:14:33","guid":{"rendered":"http:\/\/waurimal.kr\/?p=662"},"modified":"2026-01-04T23:14:34","modified_gmt":"2026-01-04T14:14:34","slug":"chap-34-%ec%9d%b4%ec%9b%90-%ea%b4%80%ea%b3%84dyadic-data-%ec%97%ad%eb%8f%99%ec%84%b1-%ed%8f%89%ea%b0%80%eb%a5%bc-%ec%9c%84%ed%95%9c-%ec%a2%85%eb%8b%a8-%eb%aa%a8%ed%98%95","status":"publish","type":"post","link":"http:\/\/waurimal.kr\/?p=662","title":{"rendered":"Chap 34. \uc774\uc6d0 \uad00\uacc4(Dyadic Data) \uc5ed\ub3d9\uc131 \ud3c9\uac00\ub97c \uc704\ud55c \uc885\ub2e8 \ubaa8\ud615"},"content":{"rendered":"\n<p>\uc548\ub155\ud558\uc138\uc694! \uc774\ubc88 \ub0b4\uc6a9\uc740 <strong>&#8220;\uc774\uc6d0 \uad00\uacc4(Dyadic Data)\uc758 \uc5ed\ub3d9\uc131\uc744 \ud3c9\uac00\ud558\uae30 \uc704\ud55c \uc885\ub2e8 \ubaa8\ud615&#8221;<\/strong>\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\uc81c\ubaa9\uc774 \ub2e4\uc18c \uc5b4\ub835\uac8c \ub290\uaef4\uc9c8 \uc218 \uc788\uc9c0\ub9cc, \uac71\uc815\ud558\uc9c0 \ub9c8\uc138\uc694. \uc6b0\ub9ac \uad50\uc721 \ud604\uc7a5\uc5d0\ub294 \uc218\ub9ce\uc740 &#8216;\uad00\uacc4&#8217;\uac00 \uc874\uc7ac\ud569\ub2c8\ub2e4. \uad50\uc0ac\uc640 \ud559\uc0dd, \uc0c1\ub2f4\uc0ac\uc640 \ub0b4\ub2f4\uc790, \ub610\ub294 \ud559\uc2b5 \ub3d9\ub8cc \uac04\uc758 \uad00\uacc4\uac00 \uc2dc\uac04\uc5d0 \ub530\ub77c \uc5b4\ub5bb\uac8c \ubcc0\ud558\uace0 \uc11c\ub85c \uc601\ud5a5\uc744 \uc8fc\uace0\ubc1b\ub294\uc9c0 \uc218\ud559\uc801\uc73c\ub85c \ubaa8\ub378\ub9c1\ud558\ub294 \ubc29\ubc95\uc744 \uc544\uc8fc \uc27d\uac8c \ud480\uc5b4\uc11c \uc124\uba85\ud574 \ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\ubcf8 \ucc55\ud130\uc5d0\uc11c \ub2e4\ub8e8\ub294 <strong>\uc5f0\uc18d\uc2dc\uac04 \ubbf8\ubd84\ubc29\uc815\uc2dd(Differential Equation Models)<\/strong>\uc740 \ub9e4\uc6b0 \uace0\uae09 \ud1b5\uacc4 \uae30\ubc95\uc73c\ub85c \uc774 \ubaa8\ud615\uc744 \uad6c\ud604\ud560 \uc218 \uc788\ub294 \ud45c\uc900 \ub3c4\uad6c\uc778 <strong>R<\/strong>\uc744 \uc0ac\uc6a9\ud558\uc5ec \uad50\uc721\uc801 \uc0c1\ud669\uc744 \uac00\uc815\ud55c \ubaa8\uc758 \ub370\uc774\ud130\ub97c \uc0dd\uc131\ud558\uace0 \ubd84\uc11d\ud558\ub294 \uacfc\uc815\uc744 \ubcf4\uc5ec\ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">1. \uad50\uc721 \ud604\uc7a5\uc5d0\uc11c\uc758 &#8216;\uad00\uacc4&#8217;\uc640 &#8216;\uc2dc\uac04&#8217;<\/h2>\n\n\n\n<p>\uc0ac\ud68c\uacfc\ud559\uacfc \ud589\ub3d9\uacfc\ud559 \uc5f0\uad6c\ub294 \uc885\uc885 \uc5ec\ub7ec \uac1c\uccb4 \uac04\uc758 \uad00\uacc4\uc5d0 \ucd08\uc810\uc744 \ub9de\ucda5\ub2c8\ub2e4. \uc5ec\uae30\uc11c <strong>&#8220;\uc774\uc6d0 \uad00\uacc4(Dyadic relationship)&#8221;<\/strong>\ub780 \ub450 \uac1c\uccb4, \uc608\ub97c \ub4e4\uc5b4 \ubd80\ubaa8-\uc790\ub140, \ub0a8\ud3b8-\uc544\ub0b4, \uadf8\ub9ac\uace0 \uad50\uc721\uc801\uc73c\ub85c\ub294 <strong>\uad50\uc0ac-\ud559\uc0dd<\/strong>\uc774\ub098 <strong>\ub3d9\ub8cc \ud559\uc2b5\uc790<\/strong> \uac04\uc758 \uad00\uacc4\ub97c \uc758\ubbf8\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\uc774 \ub450 \uc0ac\ub78c\uc758 \uc2ec\ub9ac\uc801, \ud589\ub3d9\uc801 \uacfc\uc815\uc774 \uc2dc\uac04\uc5d0 \ub530\ub77c \uc5b4\ub5bb\uac8c \uc9c4\ud654\ud558\ub294\uc9c0 \ud3c9\uac00\ud558\uae30 \uc704\ud574 \uc6b0\ub9ac\ub294 \ub370\uc774\ud130\ub97c \uc218\uc9d1\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\ud328\ub110 \ub370\uc774\ud130(Panel Data):<\/strong> \ub744\uc5c4\ub744\uc5c4 \uba87 \ubc88 \uce21\uc815\ud558\ub294 \uacbd\uc6b0 (\uc608: \ud559\uae30 \ucd08, \ud559\uae30 \ub9d0).<\/li>\n\n\n\n<li><strong>\uc9d1\uc911 \uc885\ub2e8 \ub370\uc774\ud130(Intensive Longitudinal Data):<\/strong> \uc9e7\uc740 \uae30\uac04 \ub3d9\uc548 \uc9d1\uc911\uc801\uc73c\ub85c \uce21\uc815\ud558\ub294 \uacbd\uc6b0 (\uc608: \uc218\uc5c5 \uc2dc\uac04 \ub3d9\uc548\uc758 \uc2e4\uc2dc\uac04 \uc0c1\ud638\uc791\uc6a9).<\/li>\n<\/ul>\n\n\n\n<p>\uc6b0\ub9ac\uc758 \ubaa9\ud45c\ub294 \ub450 \uad6c\uc131\uc6d0 \uac04\uc758 \uc2dc\uac04\uc801 \uc0c1\ud638\uc791\uc6a9 \uc21c\uc11c\ub97c \ud30c\uc545\ud558\uace0, \uc11c\ub85c\uac00 \uc11c\ub85c\uc5d0\uac8c \uc5b4\ub5bb\uac8c \uc601\ud5a5\uc744 \ubbf8\uce58\ub294\uc9c0 \uc778\uacfc\uad00\uacc4\ub97c \ucd94\ub860\ud558\ub294 \uac83\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1.1 \uc774\uc0b0 \uc2dc\uac04(Discrete Time) vs. \uc5f0\uc18d \uc2dc\uac04(Continuous Time)<\/h3>\n\n\n\n<p>\uc804\ud1b5\uc801\uc778 \uad6c\uc870\ubc29\uc815\uc2dd(SEM)\uc740 \uc8fc\ub85c <strong>\uc774\uc0b0 \uc2dc\uac04<\/strong> \ubaa8\ud615\uc744 \uc0ac\uc6a9\ud569\ub2c8\ub2e4. \uc774\ub294 \uc2dc\uac04\uc744 \uc815\uc218(1\ud68c\ucc28, 2\ud68c\ucc28&#8230;)\ub85c \ubd05\ub2c8\ub2e4. \ud558\uc9c0\ub9cc \uc774 \ubc29\uc2dd\uc740 &#8220;\uce21\uc815 \uac04\uaca9\uc774 \ub3d9\uc77c\ud558\ub2e4&#8221;\ub294 \uac00\uc815\uc744 \uc804\uc81c\ub85c \ud558\ub294\ub370, \ud604\uc2e4\uc5d0\uc11c\ub294 \uc9c0\ud0a4\uae30 \uc5b4\ub835\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p>\ubc18\uba74, \uc624\ub298 \uc6b0\ub9ac\uac00 \ub2e4\ub8f0 <strong>\ubbf8\ubd84\ubc29\uc815\uc2dd \ubaa8\ud615(Differential Equation Models)<\/strong>\uc740 <strong>\uc5f0\uc18d \uc2dc\uac04<\/strong>\uc744 \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uc2dc\uac04\uc740 \uc2e4(Real) \uc218\ub85c \ud45c\ud604\ub429\ub2c8\ub2e4.<\/li>\n\n\n\n<li>\ubcc0\ud654\ub294 \uc18d\ub3c4\ub098 \uac00\uc18d\ub3c4\uc640 \uac19\uc740 <strong>\ubbf8\ubd84(Derivative)<\/strong>\uc73c\ub85c \ud45c\ud604\ub429\ub2c8\ub2e4.<\/li>\n\n\n\n<li>\uce21\uc815 \uac04\uaca9\uc774 \ubd88\uaddc\uce59\ud574\ub3c4(\uc608: \ud559\uc0dd\uc774 \ud3b8\ud55c \uc2dc\uac04\uc5d0 \uc751\ub2f5\ud558\ub294 \uacbd\uc6b0) \ubb38\uc81c\uac00 \uc5c6\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n<li>\ubb34\uc5c7\ubcf4\ub2e4 \ubcc0\ud654\uc758 \uacfc\uc815\uc774 &#8216;\uba48\ucd94\uc9c0 \uc54a\uace0 \uacc4\uc18d\ub41c\ub2e4&#8217;\ub294 \uc790\uc5f0 \ud604\uc0c1\uc744 \ub354 \uc798 \ubc18\uc601\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<p>\ubcf8 \ucc55\ud130\uc5d0\uc11c\ub294 \uad50\uc721\uc801 \uc0c1\ud669\uc5d0 \uc801\uc6a9\ud560 \uc218 \uc788\ub294 4\uac00\uc9c0 \uc8fc\uc694 \uc5ed\ub3d9 \ubaa8\ud615\uc744 R \ucf54\ub4dc\uc640 \ud568\uaed8 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2. \ud611\ub825\uacfc \uc870\uc808\uc758 \ubaa8\ud615 (Models of Cooperation)<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">2.1 \ub3d9\uae30\ud654 \ubaa8\ud615 (Synchrony Model)<\/h3>\n\n\n\n<p>\uc774 \ubaa8\ud615\uc740 \ub450 \uc0ac\ub78c\uc774 \uc11c\ub85c\uc758 \ud589\ub3d9\uc774\ub098 \ubaa9\ud45c(\uc774\uc0c1\uc801 \uc0c1\ud0dc)\uc5d0 \ub9de\ucdb0 \uc790\uc2e0\uc758 \uc0c1\ud0dc\ub97c \uc870\uc815\ud558\ub294 \uacfc\uc815\uc744 \uc124\uba85\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\ubaa8\ud615 \uc218\uc2dd<\/h4>\n\n\n\n<p><math data-latex=\"\\frac{dx_{1}(t)}{dt} = a_{1}(x_{1}^{*} - x_{1}(t)) + b_{1}(x_{2}(t) - x_{1}(t))\"><semantics><mrow><mfrac><mrow><mi>d<\/mi><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><msub><mi>a<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msubsup><mi>x<\/mi><mn>1<\/mn><mo lspace=\"0em\" rspace=\"0em\">\u2217<\/mo><\/msubsup><mo>\u2212<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><msub><mi>b<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{dx_{1}(t)}{dt} = a_{1}(x_{1}^{*} &#8211; x_{1}(t)) + b_{1}(x_{2}(t) &#8211; x_{1}(t))<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\frac{dx_{2}(t)}{dt} = a_{2}(x_{2}^{*} - x_{2}(t)) + b_{2}(x_{1}(t) - x_{2}(t))\"><semantics><mrow><mfrac><mrow><mi>d<\/mi><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><msub><mi>a<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msubsup><mi>x<\/mi><mn>2<\/mn><mo lspace=\"0em\" rspace=\"0em\">\u2217<\/mo><\/msubsup><mo>\u2212<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><msub><mi>b<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{dx_{2}(t)}{dt} = a_{2}(x_{2}^{*} &#8211; x_{2}(t)) + b_{2}(x_{1}(t) &#8211; x_{2}(t))<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"x_1, x_2\"><semantics><mrow><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">x_1, x_2<\/annotation><\/semantics><\/math>: \ub450 \uc0ac\ub78c\uc758 \ud604\uc7ac \uc0c1\ud0dc.<\/li>\n\n\n\n<li><math data-latex=\"x_1^*, x_2^*\"><semantics><mrow><msubsup><mi>x<\/mi><mn>1<\/mn><mo>\u2217<\/mo><\/msubsup><mo separator=\"true\">,<\/mo><msubsup><mi>x<\/mi><mn>2<\/mn><mo form=\"prefix\" stretchy=\"false\">\u2217<\/mo><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">x_1^*, x_2^*<\/annotation><\/semantics><\/math>: \uac01\uc790\uc758 \uc774\uc0c1\uc801\uc778 \ubaa9\ud45c \uc0c1\ud0dc(\ud3c9\ud615\uc810).<\/li>\n\n\n\n<li><math data-latex=\"a\"><semantics><mi>a<\/mi><annotation encoding=\"application\/x-tex\">a<\/annotation><\/semantics><\/math>: \uc790\uc2e0\uc758 \ubaa9\ud45c\ub97c \ud5a5\ud574 \uc5bc\ub9c8\ub098 \ube68\ub9ac \ub098\uc544\uac00\ub294\uac00 (\uc790\uae30 \uc870\uc808).<\/li>\n\n\n\n<li><math data-latex=\"b\"><semantics><mi>b<\/mi><annotation encoding=\"application\/x-tex\">b<\/annotation><\/semantics><\/math>: \uc0c1\ub300\ubc29\uc758 \uc0c1\ud0dc\uc5d0 \uc5bc\ub9c8\ub098 \uc601\ud5a5\uc744 \ubc1b\uc544 \ubcc0\ud654\ud558\ub294\uac00 (\uc0c1\ud638 \uc870\uc808).<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">[\uad50\uc721\uc801 \uc608\uc2dc] \uc2e0\uaddc \uad50\uc0ac\uc640 \uba58\ud1a0 \uad50\uc0ac<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uc0c1\ud669:<\/strong> \uc5f4\uc815\uc801\uc774\uc9c0\ub9cc \uacbd\ud5d8\uc774 \ubd80\uc871\ud55c &#8216;\uc2e0\uaddc \uad50\uc0ac(<math data-latex=\"x_1\"><semantics><msub><mi>x<\/mi><mn>1<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_1<\/annotation><\/semantics><\/math>)&#8217;\uc640 \ub178\ub828\ud55c &#8216;\uba58\ud1a0 \uad50\uc0ac(<math data-latex=\"x_2\"><semantics><msub><mi>x<\/mi><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_2<\/annotation><\/semantics><\/math>)&#8217;\uac00 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uc2dc\ub098\ub9ac\uc624:<\/strong> \uc2e0\uaddc \uad50\uc0ac\ub294 \uba58\ud1a0 \uad50\uc0ac\uc758 \ub192\uc740 \uc218\uc5c5 \ud6a8\ub2a5\uac10\uc744 \ub2ee\uc544\uac00\ub824 \ud569\ub2c8\ub2e4(<math data-latex=\"b_1 &gt; 0\"><semantics><mrow><msub><mi>b<\/mi><mn>1<\/mn><\/msub><mo>&gt;<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">b_1 &gt; 0<\/annotation><\/semantics><\/math>). \ubc18\uba74 \uba58\ud1a0 \uad50\uc0ac\ub294 \uc774\ubbf8 \uc548\uc815\ub418\uc5b4 \uc788\uc5b4 \uc2e0\uaddc \uad50\uc0ac\uc5d0\uac8c \ud06c\uac8c \uc601\ud5a5\uc744 \ubc1b\uc9c0 \uc54a\uc2b5\ub2c8\ub2e4(<math data-latex=\"b_2 \\approx 0\"><semantics><mrow><msub><mi>b<\/mi><mn>2<\/mn><\/msub><mo>\u2248<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">b_2 \\approx 0<\/annotation><\/semantics><\/math>). \uc774\ub97c <strong>\ub2e8\ubc29\ud5a5 \uc18c\ud1b5(Unidirectional Communication)<\/strong>\uc774\ub77c\uace0 \ubcfc \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">R \uc2dc\ubbac\ub808\uc774\uc158 \ubc0f \uc2dc\uac01\ud654<\/h4>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>library(deSolve)\nlibrary(ggplot2)\nlibrary(tidyr)\n\n# \ubaa8\ub378 \uc815\uc758 (\ub3d9\uae30\ud654 \ubaa8\ud615)\nsynchrony_model &lt;- function(t, state, parameters) {\n  with(as.list(c(state, parameters)), {\n    # x1: \uc2e0\uaddc \uad50\uc0ac\uc758 \ud6a8\ub2a5\uac10, x2: \uba58\ud1a0 \uad50\uc0ac\uc758 \ud6a8\ub2a5\uac10\n    dx1 &lt;- a1 * (target1 - x1) + b1 * (x2 - x1)\n    dx2 &lt;- a2 * (target2 - x2) + b2 * (x1 - x2)\n    list(c(dx1, dx2))\n  })\n}\n\n# \ud30c\ub77c\ubbf8\ud130 \uc124\uc815 (\ub2e8\ubc29\ud5a5 \uc601\ud5a5: \uba58\ud1a0 -&gt; \uc2e0\uaddc)\npars &lt;- c(a1 = 0.5, target1 = 50, b1 = 0.8, # \uc2e0\uaddc \uad50\uc0ac\ub294 \uba58\ud1a0\uc5d0\uac8c \uc601\ud5a5\uc744 \ub9ce\uc774 \ubc1b\uc74c\n          a2 = 0.5, target2 = 80, b2 = 0.0) # \uba58\ud1a0\ub294 \uc601\ud5a5\ubc1b\uc9c0 \uc54a\uc74c\n\n# \ucd08\uae30\uac12 (\uc2e0\uaddc \uad50\uc0ac: 30, \uba58\ud1a0: 80)\nstate &lt;- c(x1 = 30, x2 = 80)\ntimes &lt;- seq(0, 20, by = 0.1)\n\n# \uc2dc\ubbac\ub808\uc774\uc158\nout &lt;- ode(y = state, times = times, func = synchrony_model, parms = pars)\nout_df &lt;- as.data.frame(out)\n\n# \uadf8\ub798\ud504 \uadf8\ub9ac\uae30\nggplot(out_df, aes(x = time)) +\n  geom_line(aes(y = x1, color = \"Novice Teacher\"), size = 1.2) +\n  geom_line(aes(y = x2, color = \"Mentor Teacher\"), size = 1.2, linetype = \"dashed\") +\n  labs(title = \"Synchrony Model: Mentoring Effect\",\n       y = \"Teaching Efficacy\", x = \"Time (Weeks)\") +\n  theme_minimal()\n<\/code><\/pre>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\ud574\uc11d:<\/strong> \uc704 \ucf54\ub4dc\ub97c \uc2e4\ud589\ud558\uba74, \ucd08\uae30 \ud6a8\ub2a5\uac10\uc774 \ub0ae\uc558\ub358 \uc2e0\uaddc \uad50\uc0ac(<math data-latex=\"x_1\"><semantics><msub><mi>x<\/mi><mn>1<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_1<\/annotation><\/semantics><\/math>)\uac00 \uc2dc\uac04\uc774 \uc9c0\ub0a8\uc5d0 \ub530\ub77c \uba58\ud1a0 \uad50\uc0ac(<math data-latex=\"x_2\"><semantics><msub><mi>x<\/mi><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_2<\/annotation><\/semantics><\/math>)\uc758 \uc218\uc900\uc73c\ub85c \ud6a8\ub2a5\uac10\uc774 \uc0c1\uc2b9\ud558\uc5ec \ub3d9\uae30\ud654\ub418\ub294 \uace1\uc120\uc744 \ubcfc \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n<\/blockquote>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-c74d5ab1-1eb2-4f54-b7a0-e77a3208c8bf\" href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap34.csv\">chap34<\/a><a href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap34.csv\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-c74d5ab1-1eb2-4f54-b7a0-e77a3208c8bf\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"673\" height=\"789\" src=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-1.png\" alt=\"\" class=\"wp-image-664\" srcset=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-1.png 673w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-1-256x300.png 256w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-1-624x732.png 624w\" sizes=\"auto, (max-width: 673px) 100vw, 673px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">2.2 \uc0c1\ub9ac\uacf5\uc0dd \ubaa8\ud615 (Mutualism Model)<\/h3>\n\n\n\n<p>\uc0dd\ud0dc\ud559\uc5d0\uc11c \uafc0\ubc8c\uacfc \uaf43\ucc98\ub7fc \uc11c\ub85c \ub3d5\ub294 \uad00\uacc4\ub97c \ub9d0\ud569\ub2c8\ub2e4. \uad50\uc721\uc5d0\uc11c\ub294 <strong>\ud611\ub3d9 \ud559\uc2b5<\/strong>\uc774 \ub300\ud45c\uc801\uc785\ub2c8\ub2e4. \ud63c\uc790 \uacf5\ubd80\ud560 \ub54c\ubcf4\ub2e4 \ub458\uc774 \ud568\uaed8\ud560 \ub54c \uc2dc\ub108\uc9c0\uac00 \ub098\uc11c \uac01\uc790\uc758 \ud55c\uacc4(<math data-latex=\"K\"><semantics><mi>K<\/mi><annotation encoding=\"application\/x-tex\">K<\/annotation><\/semantics><\/math>)\ub97c \ub6f0\uc5b4\ub118\ub294 \uacbd\uc6b0\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\ubaa8\ud615 \uc218\uc2dd<\/h4>\n\n\n\n<p><math data-latex=\"\\frac{dx_{1}(t)}{dt} = r_{1}x_{1}(t)[1 - \\frac{(x_{1}(t) - \\alpha_{12}x_{2}(t))}{K_{1}}]\"><semantics><mrow><mfrac><mrow><mi>d<\/mi><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><msub><mi>r<\/mi><mn>1<\/mn><\/msub><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><msub><mi>\u03b1<\/mi><mn>12<\/mn><\/msub><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><msub><mi>K<\/mi><mn>1<\/mn><\/msub><\/mfrac><mo form=\"postfix\" stretchy=\"false\">]<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{dx_{1}(t)}{dt} = r_{1}x_{1}(t)[1 &#8211; \\frac{(x_{1}(t) &#8211; \\alpha_{12}x_{2}(t))}{K_{1}}]<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uc774 \uc2dd\uc740 \ub85c\uc9c0\uc2a4\ud2f1 \uc131\uc7a5 \uace1\uc120(S\uc790\ud615 \uc131\uc7a5)\uc744 \ud655\uc7a5\ud55c \uac83\uc785\ub2c8\ub2e4.<\/li>\n\n\n\n<li><math data-latex=\"\\alpha_{12}\"><semantics><msub><mi>\u03b1<\/mi><mn>12<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\\alpha_{12}<\/annotation><\/semantics><\/math>: \uc0c1\ub300\ubc29(<math data-latex=\"x_2\"><semantics><msub><mi>x<\/mi><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_2<\/annotation><\/semantics><\/math>)\uc774 \ub098(<math data-latex=\"x_1\"><semantics><msub><mi>x<\/mi><mn>1<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_1<\/annotation><\/semantics><\/math>)\uc5d0\uac8c \uc8fc\ub294 \uc774\uc775. \uc774 \uac12\uc774 \uc591\uc218\uc774\uba74 \ub098\uc758 \uc131\uc7a5 \ud55c\uacc4\uce58(<math data-latex=\"K_1\"><semantics><msub><mi>K<\/mi><mn>1<\/mn><\/msub><annotation encoding=\"application\/x-tex\">K_1<\/annotation><\/semantics><\/math>)\ub97c \ub118\uc5b4\uc124 \uc218 \uc788\uac8c \ub3c4\uc640\uc90d\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">[\uad50\uc721\uc801 \uc608\uc2dc] \ud504\ub85c\uc81d\ud2b8 \ud300 \ud65c\ub3d9<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uc0c1\ud669:<\/strong> \ud559\uc0dd A\uc640 \ud559\uc0dd B\uac00 \uacfc\ud559 \ud504\ub85c\uc81d\ud2b8\ub97c \ud569\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uc2dc\ub098\ub9ac\uc624:<\/strong> \ud63c\uc790 \ud558\uba74 70\uc810(<math data-latex=\"K\"><semantics><mi>K<\/mi><annotation encoding=\"application\/x-tex\">K<\/annotation><\/semantics><\/math>) \uc815\ub3c4 \ubc1b\uc744 \ud559\uc0dd\ub4e4\uc774\uc9c0\ub9cc, \uc11c\ub85c \uc544\uc774\ub514\uc5b4\ub97c \uacf5\uc720\ud558\uba70(<math data-latex=\"\\alpha &gt; 0\"><semantics><mrow><mi>\u03b1<\/mi><mo>&gt;<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha &gt; 0<\/annotation><\/semantics><\/math>) 90\uc810 \uc218\uc900\uc73c\ub85c \uc131\uacfc\uac00 \ud5a5\uc0c1\ub429\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">R \uc2dc\ubbac\ub808\uc774\uc158<\/h4>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \ubaa8\ub378 \uc815\uc758 (\uc0c1\ub9ac\uacf5\uc0dd)\nmutualism_model &lt;- function(t, state, parameters) {\n  with(as.list(c(state, parameters)), {\n    # \ub85c\uc9c0\uc2a4\ud2f1 \uc131\uc7a5\uc5d0 \uc0c1\ud638\uc791\uc6a9 \ud56d \ucd94\uac00\n    dx1 &lt;- r1 * x1 * (1 - (x1 - alpha12 * x2) \/ K1)\n    dx2 &lt;- r2 * x2 * (1 - (x2 - alpha21 * x1) \/ K2)\n    list(c(dx1, dx2))\n  })\n}\n\n# \ud30c\ub77c\ubbf8\ud130 (\uc0c1\ud638 \uc774\uc775 \ubc1c\uc0dd)\npars_mut &lt;- c(r1 = 0.5, K1 = 70, alpha12 = 0.3, # \ud559\uc0dd A\n              r2 = 0.5, K2 = 70, alpha21 = 0.3) # \ud559\uc0dd B\n\nstate_mut &lt;- c(x1 = 10, x2 = 10) # \ucd08\uae30 \uc9c0\uc2dd \uc218\uc900\ntimes &lt;- seq(0, 20, by = 0.1)\n\nout_mut &lt;- ode(y = state_mut, times = times, func = mutualism_model, parms = pars_mut)\nout_mut_df &lt;- as.data.frame(out_mut)\n\n# \uadf8\ub798\ud504\nggplot(out_mut_df, aes(x = time)) +\n  geom_line(aes(y = x1, color = \"Student A\"), size = 1.2) +\n  geom_line(aes(y = x2, color = \"Student B\"), size = 1.2, linetype = \"dashed\") +\n  geom_hline(yintercept = 70, linetype = \"dotted\", color = \"gray\") + # \uc6d0\ub798 \ud55c\uacc4\uce58\n  annotate(\"text\", x = 0, y = 72, label = \"Original Capacity (K)\", hjust=0) +\n  labs(title = \"Mutualism Model: Cooperative Learning\",\n       subtitle = \"Students exceed their individual capacity (K=70)\",\n       y = \"Project Performance\", x = \"Time\") +\n  theme_minimal()\n<\/code><\/pre>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\ud574\uc11d:<\/strong> \uadf8\ub798\ud504\uc5d0\uc11c \ub450 \ud559\uc0dd\uc758 \uc131\ucde8\ub3c4\ub294 \uc6d0\ub798 \ud55c\uacc4\uc778 70\uc810\uc744 \ub118\uc5b4 \uacc4\uc18d \uc0c1\uc2b9\ud558\uc5ec \ub354 \ub192\uc740 \ud3c9\ud615\uc810\uc5d0 \ub3c4\ub2ec\ud558\uac8c \ub429\ub2c8\ub2e4. \uc774\uac83\uc774 \ud611\ub3d9\uc758 \ud798\uc785\ub2c8\ub2e4.<\/p>\n<\/blockquote>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-1d3ec93d-07e2-4ce9-8b4f-ed52bb423b47\" href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap34-2.csv\">chap34-2<\/a><a href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap34-2.csv\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-1d3ec93d-07e2-4ce9-8b4f-ed52bb423b47\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"673\" height=\"789\" src=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-2.png\" alt=\"\" class=\"wp-image-666\" srcset=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-2.png 673w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-2-256x300.png 256w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-2-624x732.png 624w\" sizes=\"auto, (max-width: 673px) 100vw, 673px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">3. \uacbd\uc7c1 \ubaa8\ud615 (Models of Competition)<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">3.1 \uc9c1\uc811 \uac04\uc12d \uacbd\uc7c1 \ubaa8\ud615 (Competition by Direct Interference)<\/h3>\n\n\n\n<p>\uc0c1\ub9ac\uacf5\uc0dd \ubaa8\ud615\uacfc \uc218\uc2dd\uc740 \uac70\uc758 \uac19\uc9c0\ub9cc, \uc0c1\ud638\uc791\uc6a9 \ud56d\uc758 \ubd80\ud638\uac00 \ubc18\ub300\uc785\ub2c8\ub2e4. \uc0c1\ub300\ubc29\uc758 \uc874\uc7ac\uac00 \ub098\uc758 \uc131\uc7a5\uc744 \ubc29\ud574\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\ubaa8\ud615 \uc218\uc2dd<\/h4>\n\n\n\n<p><math data-latex=\"\\frac{dx_{1}(t)}{dt} = r_{1}x_{1}(t)[1 - \\frac{(x_{1}(t) + \\alpha_{12}x_{2}(t))}{K_{1}}]\"><semantics><mrow><mfrac><mrow><mi>d<\/mi><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><msub><mi>r<\/mi><mn>1<\/mn><\/msub><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><msub><mi>\u03b1<\/mi><mn>12<\/mn><\/msub><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><msub><mi>K<\/mi><mn>1<\/mn><\/msub><\/mfrac><mo form=\"postfix\" stretchy=\"false\">]<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{dx_{1}(t)}{dt} = r_{1}x_{1}(t)[1 &#8211; \\frac{(x_{1}(t) + \\alpha_{12}x_{2}(t))}{K_{1}}]<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uc5ec\uae30\uc11c <math data-latex=\"+\\alpha_{12}x_2\"><semantics><mrow><mo>+<\/mo><msub><mi>\u03b1<\/mi><mn>12<\/mn><\/msub><msub><mi>x<\/mi><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">+\\alpha_{12}x_2<\/annotation><\/semantics><\/math> \ud56d\uc740 \uc0c1\ub300\ubc29\uc774 \uc874\uc7ac\ud560\uc218\ub85d \ub098\uc758 \uc131\uc7a5\ub960\uc744 \uac09\uc544\uba39\ub294\ub2e4\ub294 \uac83\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">[\uad50\uc721\uc801 \uc608\uc2dc] \uc0c1\ub300\ud3c9\uac00\uc640 \ub4f1\uc218 \uacbd\uc7c1<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\uc0c1\ud669:<\/strong> \uc804\uad50 1\ub4f1\uc744 \ub450\uace0 \ub2e4\ud22c\ub294 \ud559\uc0dd A\uc640 \ud559\uc0dd B.<\/li>\n\n\n\n<li><strong>\uc2dc\ub098\ub9ac\uc624:<\/strong> \ud55c \ud559\uc0dd\uc758 \uc131\uc801\uc774 \uc624\ub974\uba74 \uc2ec\ub9ac\uc801 \uc555\ubc15\uac10\uc774\ub098 \uc790\uc6d0(\uc120\uc0dd\ub2d8\uc758 \uad00\uc2ec \ub4f1)\uc758 \ubd84\uc0b0\uc73c\ub85c \uc778\ud574 \ub2e4\ub978 \ud559\uc0dd\uc758 \uc131\ucde8\ub3c4\uac00 \uc800\ud574\ub420 \uc218 \uc788\uc2b5\ub2c8\ub2e4. <math data-latex=\"\\alpha\"><semantics><mi>\u03b1<\/mi><annotation encoding=\"application\/x-tex\">\\alpha<\/annotation><\/semantics><\/math> \uac12\uc774 \ud06c\ub2e4\uba74 \ud55c \uba85\uc740 \uacb0\uad6d \ub3c4\ud0dc(\uc131\ucde8\ub3c4 \ud558\ub77d)\ub420 \uc218\ub3c4 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">4. \uc74c\uc758 \ud53c\ub4dc\ubc31 \ubaa8\ud615 (Negative Feedback Model)<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">4.1 \ud3ec\uc2dd\uc790-\ud53c\uc2dd\uc790 \ubaa8\ud615 (Predator-Prey Model)<\/h3>\n\n\n\n<p>\uc0dd\ud0dc\ud559\uc758 \uace0\uc804\uc801\uc778 \ub85c\ud2b8\uce74-\ubcfc\ud14c\ub77c(Lotka-Volterra) \ubaa8\ud615\uc785\ub2c8\ub2e4. \ud53c\uc2dd\uc790(\uba39\uc774)\uac00 \ub298\uc5b4\ub098\uba74 \ud3ec\uc2dd\uc790\uac00 \ub298\uc5b4\ub098\uace0, \ud3ec\uc2dd\uc790\uac00 \ub298\uc5b4\ub098\uba74 \ud53c\uc2dd\uc790\uac00 \uc904\uc5b4\ub4dc\ub294 \uc21c\ud658 \uace0\ub9ac\ub97c \uac00\uc9d1\ub2c8\ub2e4. \uad50\uc721\uc2ec\ub9ac\ud559\uc5d0\uc11c\ub294 \uc790\uae30 \uc870\uc808(self-regulation)\uc774\ub098 \uac10\uc815\uc758 \uae30\ubcf5\uc744 \uc124\uba85\ud560 \ub54c \uc720\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\ubaa8\ud615 \uc218\uc2dd<\/h4>\n\n\n\n<p><math data-latex=\"\\frac{dx_{1}(t)}{dt} = rx_{1}(t) - cx_{1}(t)x_{2}(t) \\quad (\\text{Prey})\"><semantics><mrow><mfrac><mrow><mi>d<\/mi><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mi>r<\/mi><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mi>c<\/mi><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mspace width=\"1em\"><\/mspace><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mtext>Prey<\/mtext><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{dx_{1}(t)}{dt} = rx_{1}(t) &#8211; cx_{1}(t)x_{2}(t) \\quad (\\text{Prey})<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\frac{dx_{2}(t)}{dt} = bx_{1}(t)x_{2}(t) - mx_{2}(t) \\quad (\\text{Predator})\"><semantics><mrow><mfrac><mrow><mi>d<\/mi><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mi>b<\/mi><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mi>m<\/mi><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mspace width=\"1em\"><\/mspace><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mtext>Predator<\/mtext><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{dx_{2}(t)}{dt} = bx_{1}(t)x_{2}(t) &#8211; mx_{2}(t) \\quad (\\text{Predator})<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">[\uad50\uc721\uc801 \uc608\uc2dc] \uc2dc\ud5d8 \ubd88\uc548(Prey)\uacfc \uacf5\ubd80 \uc2dc\uac04(Predator)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Prey (<\/strong><math data-latex=\"x_1\"><semantics><msub><mi>x<\/mi><mn>1<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_1<\/annotation><\/semantics><\/math><strong>): \uc2dc\ud5d8 \ubd88\uc548 (\ub610\ub294 \ubbf8\ub8e8\ub294 \uc2b5\uad00)<\/strong>\n<ul class=\"wp-block-list\">\n<li>\uac00\ub9cc\ud788 \ub450\uba74 \uc790\uc5f0\uc801\uc73c\ub85c \uc99d\uac00\ud569\ub2c8\ub2e4(\ubd88\uc548\uc774 \uc2a4\uba40\uc2a4\uba40 \uc62c\ub77c\uc634).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Predator (<\/strong><math data-latex=\"x_2\"><semantics><msub><mi>x<\/mi><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_2<\/annotation><\/semantics><\/math><strong>): \uacf5\ubd80 \ud22c\uc785 \uc2dc\uac04 (\uc9d1\ud589 \uae30\ub2a5)<\/strong>\n<ul class=\"wp-block-list\">\n<li>\ubd88\uc548\uc774 \ub192\uc544\uc9c0\uba74(<math data-latex=\"x_1\"><semantics><msub><mi>x<\/mi><mn>1<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_1<\/annotation><\/semantics><\/math> \uc99d\uac00), \uc704\uae30\uac10\uc744 \ub290\uaef4 \uacf5\ubd80\ub97c \uc2dc\uc791\ud569\ub2c8\ub2e4(<math data-latex=\"x_2\"><semantics><msub><mi>x<\/mi><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_2<\/annotation><\/semantics><\/math> \uc99d\uac00).<\/li>\n\n\n\n<li>\uacf5\ubd80\ub97c \ud558\uba74(<math data-latex=\"x_2\"><semantics><msub><mi>x<\/mi><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_2<\/annotation><\/semantics><\/math> \ub192\uc74c), \ubd88\uc548\uc774 \uc7a1\uc544\uba39\ud600 \uc904\uc5b4\ub4ed\ub2c8\ub2e4(<math data-latex=\"x_1\"><semantics><msub><mi>x<\/mi><mn>1<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_1<\/annotation><\/semantics><\/math> \uac10\uc18c).<\/li>\n\n\n\n<li>\ubd88\uc548\uc774 \uc0ac\ub77c\uc9c0\uba74, \ub2e4\uc2dc \uacf5\ubd80\ub97c \uc548 \ud558\uace0 \ub189\ub2c8\ub2e4(<math data-latex=\"x_2\"><semantics><msub><mi>x<\/mi><mn>2<\/mn><\/msub><annotation encoding=\"application\/x-tex\">x_2<\/annotation><\/semantics><\/math> \uac10\uc18c, \uc790\uc5f0 \uc18c\uba78 <math data-latex=\"m\"><semantics><mi>m<\/mi><annotation encoding=\"application\/x-tex\">m<\/annotation><\/semantics><\/math>).<\/li>\n\n\n\n<li>\uacb0\uacfc\uc801\uc73c\ub85c \ub450 \ubcc0\uc218\ub294 <strong>\uc8fc\uae30\uc801\uc778 \ud30c\ub3d9(Oscillation)<\/strong>\uc744 \uadf8\ub9ac\uac8c \ub429\ub2c8\ub2e4.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">R \uc2dc\ubbac\ub808\uc774\uc158<\/h4>\n\n\n\n<p>R<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \ubaa8\ub378 \uc815\uc758 (\ud3ec\uc2dd\uc790-\ud53c\uc2dd\uc790)\npredator_prey_model &lt;- function(t, state, parameters) {\n  with(as.list(c(state, parameters)), {\n    # x1: \uc2dc\ud5d8 \ubd88\uc548(Prey), x2: \uacf5\ubd80 \uc2dc\uac04(Predator)\n    dx1 &lt;- r*x1 - c*x1*x2\n    dx2 &lt;- b*x1*x2 - m*x2\n    list(c(dx1, dx2))\n  })\n}\n\n# \ud30c\ub77c\ubbf8\ud130\npars_pp &lt;- c(r = 0.5,  # \ubd88\uc548\uc758 \uc790\uc5f0 \uc99d\uac00\uc728\n             c = 0.1,  # \uacf5\ubd80\uac00 \ubd88\uc548\uc744 \uac10\uc18c\uc2dc\ud0a4\ub294 \ud6a8\uc728\n             b = 0.1,  # \ubd88\uc548\uc774 \uacf5\ubd80\ub97c \uc720\ubc1c\ud558\ub294 \ud6a8\uc728\n             m = 0.3)  # \uacf5\ubd80 \uc911\ub2e8(\ub9dd\uac01\/\ud734\uc2dd) \ube44\uc728\n\nstate_pp &lt;- c(x1 = 10, x2 = 5) # \ucd08\uae30\uac12\ntimes &lt;- seq(0, 50, by = 0.1)\n\nout_pp &lt;- ode(y = state_pp, times = times, func = predator_prey_model, parms = pars_pp)\nout_pp_df &lt;- as.data.frame(out_pp)\n\n# \uadf8\ub798\ud504\nggplot(out_pp_df, aes(x = time)) +\n  geom_line(aes(y = x1, color = \"Test Anxiety (Prey)\"), size = 1) +\n  geom_line(aes(y = x2, color = \"Study Time (Predator)\"), size = 1, linetype = \"dashed\") +\n  labs(title = \"Predator-Prey Model: Anxiety vs. Regulation\",\n       y = \"Level\", x = \"Time\") +\n  theme_minimal()\n<\/code><\/pre>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\ud574\uc11d:<\/strong> \uadf8\ub798\ud504\ub294 \ud30c\ub3c4\ucc98\ub7fc \ucd9c\ub801\uc785\ub2c8\ub2e4. \ud559\uc0dd\uc758 \uc0c1\ud0dc\uac00 \uc548\uc815\ub418\uc9c0 \uc54a\uace0, &#8216;\ubd88\uc548\ud574\uc11c \uacf5\ubd80\ud568 <math data-latex=\"\\rightarrow\"><semantics><mo stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">\u2192<\/mo><annotation encoding=\"application\/x-tex\">\\rightarrow<\/annotation><\/semantics><\/math> \uc548\uc2ec\ub418\uc5b4\uc11c \uacf5\ubd80 \uc548 \ud568 <math data-latex=\"\\rightarrow\"><semantics><mo stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">\u2192<\/mo><annotation encoding=\"application\/x-tex\">\\rightarrow<\/annotation><\/semantics><\/math> \ub2e4\uc2dc \ubd88\uc548\ud574\uc9d0&#8217;\uc758 \uc0ac\uc774\ud074\uc744 \ubc18\ubcf5\ud558\ub294 \ud604\uc0c1\uc744 \uc218\ud559\uc801\uc73c\ub85c \ubcf4\uc5ec\uc90d\ub2c8\ub2e4.<\/p>\n<\/blockquote>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-ff8d89c8-5bf6-458f-936b-75145c68c7e5\" href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap34-3.csv\">chap34-3<\/a><a href=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/chap34-3.csv\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-ff8d89c8-5bf6-458f-936b-75145c68c7e5\">\ub2e4\uc6b4\ub85c\ub4dc<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"673\" height=\"545\" src=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-3.png\" alt=\"\" class=\"wp-image-668\" srcset=\"http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-3.png 673w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-3-300x243.png 300w, http:\/\/waurimal.kr\/wp-content\/uploads\/2026\/01\/fig34-3-624x505.png 624w\" sizes=\"auto, (max-width: 673px) 100vw, 673px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">5. \uacb0\ub860 \ubc0f \uc81c\uc5b8<\/h2>\n\n\n\n<p>\uc6b0\ub9ac\ub294 \uc774 \uc7a5\uc744 \ud1b5\ud574 <strong>\uc774\uc6d0 \uad00\uacc4(Dyadic Data)<\/strong>\ub97c \ubd84\uc11d\ud558\ub294 4\uac00\uc9c0 \uac15\ub825\ud55c \ub3c4\uad6c\ub97c \uc0b4\ud3b4\ubcf4\uc558\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\ub3d9\uae30\ud654 \ubaa8\ud615:<\/strong> \uba58\ud1a0\ub9c1 \uad00\uacc4\ucc98\ub7fc \uc11c\ub85c \ub2ee\uc544\uac00\ub294 \uacfc\uc815.<\/li>\n\n\n\n<li><strong>\uc0c1\ub9ac\uacf5\uc0dd \ubaa8\ud615:<\/strong> \ud611\ub3d9 \ud559\uc2b5\uc744 \ud1b5\ud574 \uc2dc\ub108\uc9c0\ub97c \ub0b4\ub294 \uacfc\uc815.<\/li>\n\n\n\n<li><strong>\uacbd\uc7c1 \ubaa8\ud615:<\/strong> \uc0c1\ub300\ud3c9\uac00 \uc0c1\ud669\uc5d0\uc11c \uc11c\ub85c\ub97c \uc5b5\uc81c\ud558\ub294 \uacfc\uc815.<\/li>\n\n\n\n<li><strong>\ud3ec\uc2dd\uc790-\ud53c\uc2dd\uc790 \ubaa8\ud615:<\/strong> \uac10\uc815\uacfc \ud559\uc2b5 \uc870\uc808 \uac04\uc758 \uc21c\ud658\uc801\uc778 \uc5ed\ub3d9.<\/li>\n<\/ol>\n\n\n\n<p>\uc774\ub7ec\ud55c \ubaa8\ud615\ub4e4\uc740 \uc804\ud1b5\uc801\uc778 SEM\uacfc \ub2ec\ub9ac, \uc2dc\uac04\uc758 \ud750\ub984 \uc18d\uc5d0\uc11c \ubcc0\uc218\ub4e4\uc774 \uc5b4\ub5bb\uac8c <strong>&#8216;\ubcc0\ud654&#8217;<\/strong>\ud558\ub294\uc9c0 \uadf8 \uc790\uccb4\ub97c \ubbf8\ubd84\ubc29\uc815\uc2dd(<math data-latex=\"dx\/dt\"><semantics><mrow><mi>d<\/mi><mi>x<\/mi><mi>\/<\/mi><mi>d<\/mi><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">dx\/dt<\/annotation><\/semantics><\/math>)\uc73c\ub85c \uc124\uba85\ud569\ub2c8\ub2e4. \ub370\uc774\ud130 \uc218\uc9d1 \uae30\uc220\uc758 \ubc1c\ub2ec\ub85c \uad50\uc721 \ud604\uc7a5\uc5d0\uc11c\ub3c4 \uc2a4\ub9c8\ud2b8 \uae30\uae30\ub97c \uc774\uc6a9\ud55c \uc2e4\uc2dc\uac04 \ub370\uc774\ud130(EMA) \uc218\uc9d1\uc774 \uac00\ub2a5\ud574\uc84c\uc2b5\ub2c8\ub2e4. \uc5ec\ub7ec\ubd84\ub3c4 \uc774\ub7ec\ud55c \ubaa8\ud615\uc744 \ud65c\uc6a9\ud558\uc5ec \ub2e8\uc21c\ud55c \uc0c1\uad00\uad00\uacc4\ub97c \ub118\uc5b4, \uad50\uc721\uc801 \uc0c1\ud638\uc791\uc6a9\uc758 <strong>&#8216;\uc5ed\ub3d9\uc801 \uba54\ucee4\ub2c8\uc998&#8217;<\/strong>\uc744 \ubc1d\ud600\ub0b4\ub294 \uc5f0\uad6c\uc5d0 \ub3c4\uc804\ud574 \ubcf4\uc2dc\uae38 \ubc14\ub78d\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\ucc38\uace0\ubb38\ud5cc (References)<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Chambliss, D. F., &amp; Schutt, R. K. (2018). <em>Making sense of the social world: Methods of investigation<\/em> (6th ed.). Thousand Oaks, CA: Sage.<\/li>\n\n\n\n<li>Chen, M., Song, H., &amp; Ferrer, E. (2026). Longitudinal Models for Assessing Dynamics in Dyadic Data. In <em>Chapter 34<\/em> (pp. 634-645).<\/li>\n\n\n\n<li>Cole, P. M., Bendez\u00fa, J. J., Ram, N., &amp; Chow, S.-M. (2017). Dynamical systems modeling of early childhood self-regulation. <em>Emotion, 17<\/em>(4), 684\u2013699.1<\/li>\n\n\n\n<li>Felmlee, D. H., &amp; Greenberg, D. F. (1999). A dynamic systems model of dyadic interaction. <em>Journal of Mathematical Sociology, 23<\/em>(3), 155\u2013180.<\/li>\n\n\n\n<li>Ferrer, E., &amp; Steele, J. (2014). Differential equations for evaluating theoretical models of dyadic interactions. In P. C. Molenaar, R. M. Lerner, &amp; K. M. Newell (Eds.), <em>Handbook of developmental systems theory and methodology<\/em> (pp. 345\u2013368). New York: Guilford Press.<\/li>\n\n\n\n<li>Gottman, J., Swanson, C., &amp; Murray, J. (1999). The mathematics of marital conflict: Dynamic mathematical nonlinear modeling of newlywed marital interaction. <em>Journal of Family Psychology, 13<\/em>(1), 3\u201319.<\/li>\n\n\n\n<li>Kot, M. (2001). <em>Elements of mathematical ecology<\/em>. Cambridge, UK: Cambridge University Press.<\/li>\n\n\n\n<li>Lotka, A. J. (1925). <em>Elements of physical biology<\/em>. Baltimore: Williams &amp; Wilkins.<\/li>\n\n\n\n<li>Oud, J. H. L., &amp; Singer, H. (2008). Continuous time modeling of panel data: SEM versus filter techniques. <em>Statistica Neerlandica, 62<\/em>(1), 4\u201328.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>WaurimaL\uc758 \ud55c\ub9c8\ub514:<\/strong> \uc5ec\ub7ec\ubd84, \uc218\uc2dd\uc774 \ub098\uc640\uc11c \ub2f9\ud669\ud558\uc168\uc8e0? \ud558\uc9c0\ub9cc \uc218\uc2dd\uc740 \ud604\uc0c1\uc744 \uba85\ud655\ud558\uac8c \uae30\uc220\ud558\uae30 \uc704\ud55c \uc5b8\uc5b4\uc77c \ubfd0\uc785\ub2c8\ub2e4. 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