ag-gipp/GoUldI

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{
  "constraints" : [ ],
  "math_inputtex" : "x_{n+1}=rx_n(1-x_n).",
  "math_inputtex_semantic" : "\\w{Q50701}{x}_{\\w{Q21199}{n}+1} = \\w{Q1413083}{r} x_n(1-x_n)",
  "correct_tex" : "x_{n+1}=rx_n(1-x_n)",
  "correct_mml" : "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"p1.1.m1.1\" class=\"ltx_Math\" alttext=\"x_{n+1}=rx_{n}(1-x_{n})\" display=\"inline\">\n  <semantics id=\"p1.1.m1.1a\">\n    <mrow id=\"p1.1.m1.1.13\" xref=\"p1.1.m1.1.13.cmml\">\n      <msub id=\"p1.1.m1.1.13.1\" xref=\"p1.1.m1.1.13.1.cmml\">\n        <mi id=\"p1.1.m1.1.1\" xref=\"p1.1.m1.1.1.cmml\">x</mi>\n        <mrow id=\"p1.1.m1.1.2.1\" xref=\"p1.1.m1.1.2.1.cmml\">\n          <mi id=\"p1.1.m1.1.2.1.1\" xref=\"p1.1.m1.1.2.1.1.cmml\">n</mi>\n          <mo id=\"p1.1.m1.1.2.1.2\" xref=\"p1.1.m1.1.2.1.2.cmml\">+</mo>\n          <mn id=\"p1.1.m1.1.2.1.3\" xref=\"p1.1.m1.1.2.1.3.cmml\">1</mn>\n        </mrow>\n      </msub>\n      <mo id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.3.cmml\">=</mo>\n      <mrow id=\"p1.1.m1.1.13.2\" xref=\"p1.1.m1.1.13.2.cmml\">\n        <mi id=\"p1.1.m1.1.4\" xref=\"p1.1.m1.1.4.cmml\">r</mi>\n        <mo id=\"p1.1.m1.1.13.2.1\" xref=\"p1.1.m1.1.13.2.1.cmml\">⁢</mo>\n        <msub id=\"p1.1.m1.1.13.2.2\" xref=\"p1.1.m1.1.13.2.2.cmml\">\n          <mi id=\"p1.1.m1.1.5\" xref=\"p1.1.m1.1.5.cmml\">x</mi>\n          <mi id=\"p1.1.m1.1.6.1\" xref=\"p1.1.m1.1.6.1.cmml\">n</mi>\n        </msub>\n        <mo id=\"p1.1.m1.1.13.2.1a\" xref=\"p1.1.m1.1.13.2.1.cmml\">⁢</mo>\n        <mrow id=\"p1.1.m1.1.13.2.3\" xref=\"p1.1.m1.1.13.2.3.2.cmml\">\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.7\" xref=\"p1.1.m1.1.13.2.3.2.cmml\">(</mo>\n          <mrow id=\"p1.1.m1.1.13.2.3.2\" xref=\"p1.1.m1.1.13.2.3.2.cmml\">\n            <mn id=\"p1.1.m1.1.8\" xref=\"p1.1.m1.1.8.cmml\">1</mn>\n            <mo id=\"p1.1.m1.1.9\" xref=\"p1.1.m1.1.9.cmml\">-</mo>\n            <msub id=\"p1.1.m1.1.13.2.3.2.1\" xref=\"p1.1.m1.1.13.2.3.2.1.cmml\">\n              <mi id=\"p1.1.m1.1.10\" xref=\"p1.1.m1.1.10.cmml\">x</mi>\n              <mi id=\"p1.1.m1.1.11.1\" xref=\"p1.1.m1.1.11.1.cmml\">n</mi>\n            </msub>\n          </mrow>\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.12\" xref=\"p1.1.m1.1.13.2.3.2.cmml\">)</mo>\n        </mrow>\n      </mrow>\n    </mrow>\n    <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n      <apply id=\"p1.1.m1.1.13.cmml\" xref=\"p1.1.m1.1.13\">\n        <eq id=\"p1.1.m1.1.3.cmml\" xref=\"p1.1.m1.1.3\"/>\n        <apply id=\"p1.1.m1.1.13.1.cmml\" xref=\"p1.1.m1.1.13.1\">\n          <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.13.1.1.cmml\" xref=\"p1.1.m1.1.13.1\">subscript</csymbol>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">Q50701</csymbol>\n          <apply id=\"p1.1.m1.1.2.1.cmml\" xref=\"p1.1.m1.1.2.1\">\n            <plus id=\"p1.1.m1.1.2.1.2.cmml\" xref=\"p1.1.m1.1.2.1.2\"/>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.2.1.1.cmml\" xref=\"p1.1.m1.1.2.1.1\">Q21199</csymbol>\n            <cn type=\"integer\" id=\"p1.1.m1.1.2.1.3.cmml\" xref=\"p1.1.m1.1.2.1.3\">1</cn>\n          </apply>\n        </apply>\n        <apply id=\"p1.1.m1.1.13.2.cmml\" xref=\"p1.1.m1.1.13.2\">\n          <times id=\"p1.1.m1.1.13.2.1.cmml\" xref=\"p1.1.m1.1.13.2.1\"/>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.4.cmml\" xref=\"p1.1.m1.1.4\">Q1413083</csymbol>\n          <apply id=\"p1.1.m1.1.13.2.2.cmml\" xref=\"p1.1.m1.1.13.2.2\">\n            <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.13.2.2.1.cmml\" xref=\"p1.1.m1.1.13.2.2\">subscript</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.5.cmml\" xref=\"p1.1.m1.1.5\">Q50701</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.6.1.cmml\" xref=\"p1.1.m1.1.6.1\">Q21199</csymbol>\n          </apply>\n          <apply id=\"p1.1.m1.1.13.2.3.2.cmml\" xref=\"p1.1.m1.1.13.2.3\">\n            <minus id=\"p1.1.m1.1.9.cmml\" xref=\"p1.1.m1.1.9\"/>\n            <cn type=\"integer\" id=\"p1.1.m1.1.8.cmml\" xref=\"p1.1.m1.1.8\">1</cn>\n            <apply id=\"p1.1.m1.1.13.2.3.2.1.cmml\" xref=\"p1.1.m1.1.13.2.3.2.1\">\n              <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.13.2.3.2.1.1.cmml\" xref=\"p1.1.m1.1.13.2.3.2.1\">subscript</csymbol>\n              <csymbol cd=\"latexml\" id=\"p1.1.m1.1.10.cmml\" xref=\"p1.1.m1.1.10\">Q50701</csymbol>\n              <csymbol cd=\"latexml\" id=\"p1.1.m1.1.11.1.cmml\" xref=\"p1.1.m1.1.11.1\">Q21199</csymbol>\n            </apply>\n          </apply>\n        </apply>\n      </apply>\n    </annotation-xml>\n    <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">x_{n+1}=rx_{n}(1-x_{n})</annotation>\n  </semantics>\n</math>",
  "uri" : "https://en.wikipedia.org/w/index.php?title=Bifurcation_diagram&oldid=808112333",
  "title" : "bifurcation diagram of the logistic map",
  "comment" : "NTCIR 12 wiki topic 9",
  "type" : "equation"
}