(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 50213, 1115] NotebookOptionsPosition[ 48876, 1063] NotebookOutlinePosition[ 49219, 1078] CellTagsIndexPosition[ 49176, 1075] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"f", "[", RowBox[{"n_", ",", "p_"}], "]"}], ":=", RowBox[{ RowBox[{"n", RowBox[{"(", RowBox[{"1", "-", FractionBox["n", "2"]}], ")"}]}], "-", FractionBox[ RowBox[{"n", "*", "p"}], RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "2"]}], ")"}]]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"g", "[", RowBox[{"n_", ",", "p_"}], "]"}], ":=", RowBox[{ FractionBox[ RowBox[{"n", "*", "p"}], RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "2"]}], ")"}]], "-", RowBox[{"2", "p"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"n", RowBox[{"(", RowBox[{"1", "-", FractionBox["n", "2"]}], ")"}]}], "-", FractionBox[ RowBox[{"n", "*", "p"}], RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "2"]}], ")"}]]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ FractionBox[ RowBox[{"n", "*", "p"}], RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "2"]}], ")"}]], "-", RowBox[{"2", "p"}]}], "\[Equal]", "0"}]}], ",", RowBox[{"{", RowBox[{"n", ",", "p"}], "}"}], ",", "Reals"}], "]"}], " "}]}], "Input", CellChangeTimes->{{3.6621414745188074`*^9, 3.6621415351147385`*^9}, { 3.6621632908146877`*^9, 3.662163503752867*^9}, {3.662163577785102*^9, 3.6621636655481215`*^9}, {3.6621746376582565`*^9, 3.662174639002925*^9}, { 3.6621766448111167`*^9, 3.6621766662498894`*^9}, 3.6622597909397426`*^9, { 3.6623078340201416`*^9, 3.662307986570867*^9}, {3.6623466129361596`*^9, 3.6623466536210513`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"n", "\[Rule]", "0"}], ",", RowBox[{"p", "\[Rule]", "0"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"n", "\[Rule]", "2"}], ",", RowBox[{"p", "\[Rule]", "0"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.662307784210293*^9, 3.6623079912581353`*^9, 3.6623466557930174`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"jacobianMatrix", "[", RowBox[{"n_", ",", "p_"}], "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"D", "[", RowBox[{ RowBox[{"f", "[", RowBox[{"n", ",", "p"}], "]"}], ",", "n"}], "]"}], ",", RowBox[{"D", "[", RowBox[{ RowBox[{"f", "[", RowBox[{"n", ",", "p"}], "]"}], ",", "p"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"D", "[", RowBox[{ RowBox[{"g", "[", RowBox[{"n", ",", "p"}], "]"}], ",", "n"}], "]"}], ",", RowBox[{"D", "[", RowBox[{ RowBox[{"g", "[", RowBox[{"n", ",", "p"}], "]"}], ",", "p"}], "]"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", RowBox[{"jacobianMatrix", "[", RowBox[{"n", ",", "p"}], "]"}], "]"}]}], "Input", CellChangeTimes->{{3.662163732707963*^9, 3.6621638021829367`*^9}, { 3.662163971916645*^9, 3.66216397899605*^9}, {3.662164182409684*^9, 3.66216420244083*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"1", "-", "n", "+", FractionBox[ RowBox[{"2", " ", SuperscriptBox["n", "2"], " ", "p"}], SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "2"]}], ")"}], "2"]], "-", FractionBox["p", RowBox[{"1", "+", SuperscriptBox["n", "2"]}]]}], RowBox[{"-", FractionBox["n", RowBox[{"1", "+", SuperscriptBox["n", "2"]}]]}]}, { RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"2", " ", SuperscriptBox["n", "2"], " ", "p"}], SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "2"]}], ")"}], "2"]]}], "+", FractionBox["p", RowBox[{"1", "+", SuperscriptBox["n", "2"]}]]}], RowBox[{ RowBox[{"-", "2"}], "+", FractionBox["n", RowBox[{"1", "+", SuperscriptBox["n", "2"]}]]}]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.6623077842592955`*^9, 3.6623080044488897`*^9, 3.6623466610588617`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ss1", "=", RowBox[{"jacobianMatrix", "[", RowBox[{"0", ",", "0"}], "]"}]}]], "Input", CellChangeTimes->{{3.6623077576697745`*^9, 3.662307758129801*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "2"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.6623077842782965`*^9, 3.66230802421402*^9, {3.662308708231144*^9, 3.6623087112483163`*^9}, 3.662346663980857*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Eigenvalues", "[", "ss1", "]"}]], "Input", CellChangeTimes->{{3.6621746301969433`*^9, 3.6621746534039087`*^9}, { 3.6623077607139487`*^9, 3.6623077631270866`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "1"}], "}"}]], "Output", CellChangeTimes->{3.6623077842972975`*^9, 3.6623087688489356`*^9, 3.6623466654184256`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ss2", "=", RowBox[{"jacobianMatrix", "[", RowBox[{"2", ",", "0"}], "]"}]}]], "Input", CellChangeTimes->{{3.6623089054271755`*^9, 3.6623089058483763`*^9}, { 3.6623089521180573`*^9, 3.6623089557372637`*^9}, {3.6623467090764847`*^9, 3.6623467103265257`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", FractionBox["2", "5"]}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", FractionBox["8", "5"]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.66230895941887*^9, {3.6623466874974623`*^9, 3.6623467171236954`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Eigenvalues", "[", "ss2", "]"}]], "Input", CellChangeTimes->{{3.6623089671096835`*^9, 3.6623089675308847`*^9}, { 3.66234671268601*^9, 3.662346712920395*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", FractionBox["8", "5"]}], ",", RowBox[{"-", "1"}]}], "}"}]], "Output", CellChangeTimes->{ 3.6623089686384864`*^9, {3.662346689200658*^9, 3.6623467182174892`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"u1", "=", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"f", "[", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "]"}], "\[Equal]", RowBox[{ RowBox[{"n", "'"}], "[", "t", "]"}]}], "&&", RowBox[{ RowBox[{"g", "[", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "]"}], "\[Equal]", RowBox[{ RowBox[{"p", "'"}], "[", "t", "]"}]}], "&&", RowBox[{ RowBox[{"n", "[", "0", "]"}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{"p", "[", "0", "]"}], "\[Equal]", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "10"}], "}"}]}], "]"}]}], ";"}], "\n", RowBox[{"plot1", "=", RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "}"}], "/.", "u1"}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Blue", ",", "Thick"}], "}"}]}], ",", RowBox[{"AxesOrigin", "\[Rule]", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]}]}], "Input", CellChangeTimes->{{3.662259841723117*^9, 3.662259862583359*^9}, { 3.6622598957722406`*^9, 3.6622599666189413`*^9}, 3.662260120609727*^9, { 3.662309007186154*^9, 3.662309007654155*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJw10wk0llsXB3BSZso8NFERKlOiVM9fXZQ0UaJQV5nSDbcobopMicxFGsWX RDLPF5mnMs9DMmd+TK/XkPd7Wt/6zlpn7fVbZ52z9z5nHcmrdvoWa5iYmMap +Tv+b5D4f3TzJNNYqKi8gfOKZccUlvZZF/NSTlRGKz1tCvKvtaUlKbskdelk Bk5ha9hkkzplg+G9Hu9spqAul1pmTLk0W+1MptYU5LjEZj0or+1cd48uMYWR pGy9VMoWJfubzFcmYR8q3zFC+fCUjcxK6yRy5Pg8dzKT+NGkqpWfOonCySXt vyj/Z1KVHhc4CVdDL/Esyp3p69YX3ZjEZJcOjXMNia7ow4Ysxychm9lfb055 WcHrje2OSdzUEX1fSjns4aNUFuZJXDPl5n/FQuJChIZXXM4E9F/Ev+RbSyI6 W7s3N3wC3HeiV/wpLzm91qE5TOCSm8mOl+tIiD/uvD+oMAE5m18du1hJsKnw j0TwTOCFfvbxYsr2nXpv74yN47m5rBwrO4nbzYeVYj+M43bRuYBkysqaXYkr XuN462Lre42DxPcvvflO5uPY8bfZrk5OEjpyrE1DkuP4Y+mAmigvCX8fm/Jn b8ZgkGPvvkCZVLbNlnwwhk4rE5nu9STUgl2+NZqOgVFw1TKXj7o/zYrYj5vH 4JBc3V4kRELo+NfjIm9HMZqZIdskTCL/8UubWtdRXA2UixgTITEkvuPUpz9H cbijNnu3OIm69fqxjdtGUWNSo7awhcQ5h3PMTbEjkNgVl71fgoSiSM6tBN8R +Cq/knSTJHH/ZuzpuL9GIHjhnI/EDmq96mY0j9II+BqYpmNkSYSYtJy6k/sT SlsFFEr2kTh7rW7Dp5ZhRNFkGjzUSIjlf7Y/kzWMVZ9H/ToHqHzbjt8VezGM L/nqiiOHSFwris+UuDwMs6BDfrc1Sai7qeTThoewzcw4x0KbRIbWCHdV1RCu JCwJXT5OQtPPyK0oYQhBz1uUzE5S/elZCm5zGEK3g4hI0nkSBdwPU8LWDEGg V7Os4QKJQG3eKf+hQZywHTRbNiKxPl+xI7ZqEHuUnuCyKYlIbRq7Tugg1qMs 97olCdPeyt490oOg1/LTgpxJjDZLXruqPwDl+ae1vC4k/lE6HOW6fwDDMRkb Qx6Q8Clyrc/bMoC/68MnYz1ItAWNX3w11o8Bea4U4QASSooent3e/Shtbz07 Hk2d91CL/WRxH8ruqY7nxZD4V2Fq0jy+D6UuNo+efiTxRD3l0KvQPsyEPH13 NpFE/5eKWxbmfXjQkB/Fkksifq0w72W2PkjGZDaebqTec2C7f5l+L6zTBHfu byHBL5UYKkv0wucNk5NUO9Uv63mB97K9MBbi+MXVQ/2XfybYB5l6YU5z+sU2 RqJk8NYLr6QfcBKY2J3JMo1/nXpXFQR/oCZTpaObdRqRI7t5eZh/QNRAUImd cxpnXVRimLt64F9xutxqwzS0nw5IGQX1YCotnE1/8zRMxu6tbFr+DvvUFMsa tWmsTR/WaG3rxjknv5N7Dk6DVV6R9Ux6N64WbvYLJKZRFsQ0SAZ3g/uiGcNU axqVurIKKbrdoJWzYNu5aVgd4kuXKuzC9anPU3/YTWPNbtI9JrUTGw8x91V9 nEaCIfPTwvR27DjiVu+UQNWTcbQvO7wdnQ2frWWTp3G95qVAs3M7js3tuh+S NY3FviWX20Q7ysK2VniUT2MiSoWuW9kGV25F5Z7BadzwZmY/PtiKKYnwNyY7 ZnBQrsf5z30tcMk3cTaUmYGsndmJ6xtbMOva5HR+9wxoudYHgphbYFzZ1nxe ZQZufSs/1GqaUVp3PMJWcwbdultvjlo3IyZHd2qNxQyOfH1nWRDdBDY+Q6On H2ZQz/nm0R/yjZA2zF7a+WkGKVGlUiNCjdR7cD3NS5rBP/kK1xJ+NUD1tHLE ZPYM4mxcpIK/NSDQ2uum1dcZqMx9iy+0bcA9wbHDSdMzyPqy9vv7jHr4B7rQ HhyeRd1EqeE94zr83GCScfzoLMRCQ/9N0K7DkUup3wWOzUKNy1RnSakOAWwP DT+fnYXFm4Fzvex12NzkbD97bRYsFm/nyuxqIfzR40mO7yxWD40/VNtXg0q9 EimJ9lmUsTOVCA1UY++rx29yumdR7Hi0/2dRNebXXe8x6JtFYdWv0b531dji c+VTwNgsyMDHMyf+rEakhpYYx+oszh/9UTf4vQo7RjZFbNk+B1FjmR7J/krU 7nqklnlzDpY/HkwGsFbg2GH/cvNbc3B5Ipo2NlKO0O+V+fx353BjvZmgzbdy 7AkbbbFzm8NI0/yvqqflaPIdMZEPnUOfkfdeMalysEPIJCdrDhqOhx3Kdctw 38h96zLLPDTOzrvaJpXgiGHGFiGOeVxJcXCOeVaCCa0cBQXeeUgM2fkw3SvB vXhr52ui8/gZxqokrl2C9vvX9b7unkd1k5hiT3cxnrYrmLwymEdIwX8E/QWK IdrkuU3iwzy2TLfRzMIKITOpc1T10zwy+IROBrgW4luN6oaTyfO4pB+R02pd iOdTvvF3cufR3R9xsfBgIW4xK4eW187joejFjrG+L9hPlyowoM/j/Kn8PFfV L2j+OXt2gw4NLJ8yyq715+GTv6094xQN1e4K75Xz8rB1sHxiQp+GCeutd5TC 83Beln2xwoQG48/befJ182DleJH/rj0NWbsWe7gz/0VwIL9BcjgNXZeTXpwJ ywXXbNjJgEEa5HZmP/numA2u5JBq81Ea8q7WlxIG2VhXffCq+hQNz4pdBStU snH3RFtNH52G7tjT8gZzWdizwmEnw70A23H3+XOOWajR+yrmpbyADZ/SfmQ9 yETrdHrMnQcLkLI72FuVkI73HXGWne4LMKn06PgWmg4ZPR1ZPFqA9C8Oxynn dBSnGiSzBC0gyrZ/bYB2Om4N2cW6vVvApUH9epXeNHDllm3QKVnAlLuVLNem NJy5HPOFk4MOtrTNiWMxKaCla6nwB9Lhd8907QfOJHActOvzDqXj0BHjTRZj iVjV0+dfCqfj7I7gmeTCRFiF/DXbGUlH64PJkTHbRHANr430T6HjHnupeEf1 ZzjJm1V/aKbj/iN/NevABJR8iktMEl+E7er4TNDBeOg/s5sdeLuIjPaE5DUb PwCD2+U+Ry8iPG/Y9/NqDCrWRA45fliEpvQ5H5e+GEy8WT/FlLgILodsnQdx MUgMi1dZl7+Idse0esFDMfin+r1uWeciVnieWd20eA89x2VbGeElpLuXyFfU RmPfvB6zqfcSpIQ/+R1djoTTmIV62uMltIzHtxUORUL3BBY5/JcQ5DYcfLEh EpYCFWzJoUt45dlWX/8xEl8CO8wnIpcQ6bVBq+9iJGS6ljm35i6hwa5Wt9Hl LU75yG63nFxCrcMdIkfxNSLSHk95nV3GEl9XSrpgBEZZAjUKzi2DcSm4K2f2 OfaSR9poF5bx5H7vyGjDc3T88Or603QZzQIBjVXBz9E2eomQsFlG2EDODw++ 5zgw0PPspMcyLATu1MaJhgPWzqdN05aRKj+WY6z5DLnqLv1/861gf8EVDV62 EKw7eUF5veAKUghh3XYyGEMXLgrEC6/gX5UWq4KOYCRpXPb/vnEFvSvZxl2f gyGSuXpDRXoFrcfWVRsYBYOv1EHmlfoK9m46lbkrKQimgpxal6+uoC7L+pHw YACUxViSixNWUMKTn+V51xeaSX93nMYvvDpxo8tlxB0L+9hCjLJ+4X1b5evW XfcQLKO0RIqsYmGto9/2mdsY7Hflk7VbxfOfNiH97n9hXqzg297UVXhbzEWp NJlD7O38a09yFRvqfooIRJlie+STNeLbGPjH11Jweq8BDK0PuFkcZ2AjvTiR i/UMNKyHMj7aMCBYxNy3TlwbjPCIBronA2Lrjyk0imlAsDpf0+AFA9Enmcc3 vlCDtJZL0bUEBo65vr9e2aaI1zVftyzmMvDSP77sznMZMKr9qkYqGGirDnCQ dZHEwNHigUONDByQrhDwZhHDizIdT4lOBirmr255eZIf5tNfQiT6GKgu08jR FuCE34KexZ1hBjRTlzP1mVhQlPlZsnSMgZ2zFar+3csEd1a95/MpBv6yeswv MzRLbGbRXHKfofKvfKX/yTdBXKiJthSZZ6Bb4uuN8wkDhLeKWgHPAuX07W7u wt+JuyJp/lF0Bkgnro5y1hYi2XxOi2OJAU77dZfCrWsJ+oz6CfFlqj76zomw 4TLCgsfFlGuFgSfyMwmuml8Im51sk1WUC5iDNllpZBJG+rwtJr8Y2BybE7yb kUS09FcOdlNeP3vjytN9sYShWjS3xioDfEW/No2+eUecCiyWCKSs+s5LwfZb BOEpzb2/mbL5KWXWU5YhRIydejAng6rH2S6tvs2X+LBoac1F+VYPzV8u1Zfo 1GkluCmLSg8oZfn7Euyc3iM8lEsYXT72f/gSrbx7VPko7wlpkz2T/JhoX9ie IEL57da5635hPoT+t69COyiLqMg1K3p5EzZXXrT8dlDmsc4oC29C4l1+mBRl ZULy+hFtb4L+mEdoJ+U1J2wFWNi9ib/PNHPIUbbjU7cM9vci/ngR2KRA2YJz aFtkpCeRpsvrp0j5tmtGVK6HJyHKNqGh9Hv/t45HDEtPQm/ma5wy5awhT2fG Hk/iFV367j7K26tk8tvyPIhCwwwZVcoCWWa7FaM8iLW2ce2/rXg9ZzLB24N4 IFx8YD9lDk4lq41nPYjVxp8/f9t+jjmCc58HofLWMfwAZeNwI+Gt4h5EMY+N ljplXnve10YMd0IvvWzmt+uXV0YzBtyJ/wKM6oR2 "]]}}, Axes->True, AxesLabel->{ FormBox["\"N\"", TraditionalForm], FormBox["\"P\"", TraditionalForm]}, AxesOrigin->{0, 0}, Method->{}, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{3.662307784372302*^9, 3.662308978591304*^9, 3.6623090087149568`*^9, 3.6623466919195204`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"u2", "=", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"f", "[", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "]"}], "\[Equal]", RowBox[{ RowBox[{"n", "'"}], "[", "t", "]"}]}], "&&", RowBox[{ RowBox[{"g", "[", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "]"}], "\[Equal]", RowBox[{ RowBox[{"p", "'"}], "[", "t", "]"}]}], "&&", RowBox[{ RowBox[{"n", "[", "0", "]"}], "\[Equal]", "3"}], "&&", RowBox[{ RowBox[{"p", "[", "0", "]"}], "\[Equal]", "4"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "10"}], "}"}]}], "]"}]}], ";"}], "\n", RowBox[{"plot2", "=", RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "}"}], "/.", "u2"}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Red", ",", "Dashed"}], "}"}]}], ",", RowBox[{"AxesOrigin", "\[Rule]", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]}]}], "Input", CellChangeTimes->{{3.6622599740255003`*^9, 3.662260002417307*^9}, 3.6622601176408434`*^9}], Cell[BoxData[ GraphicsBox[{{}, {}, {RGBColor[1, 0, 0], Dashing[{Small, Small}], LineBox[CompressedData[" 1:eJwl13c8Vf8fB/BLZjIzM/uGykh0jYz7vmhYWUWyqSQrhCQrpAglWwhFiIqU spUVsrNnXaLITDLO+X08fuef83g+Huee837cz+fzen8+++2vGV+mJhAIwlQE ws79/xcD+f93NvJFydZn+xboySu/Y60cv7KSfykV25mM0ZM9Hnx4wPyClSxg xC8gUUVPvrSZT2Q+z0qWMygR1vKnJx8VCK/uK2Yhlx6SzuEl0JNpzZqMNTyZ yV8mb7FrCdCRDWP4JzkFmMgs/e2cTI9pyG1ZjuOnqOnJHMuvAo5rUZNPFK59 xIkEMqGfNmPXDIHM6MyTr3/rL+h8dx+PZCKQlyb2v16VXIJFcsbJDAYCuTvH Su0z5xJkLz8vL6MlkD+Jcbys2l4E/Mprw384DlPJ5v60nYvwnFD+N3UWB04u v49MPovw45p3M20NDk0d1udTHyzAr/NT3/954KDgOzeySjUPEkbG1sGuOCgP 9KssDM2B3Fe/92xXcXBy9lwQKp0DmR/iLfq2OIjGvBURvDIH2yF7E0kGOPhc KoSojl/w0nBNZPwIDnMGFup/8n8CBHiNVq5icNtMLJM5dAaqk0dbUpcwOJk3 ZGR2aQbW/n1+H/QbA2nzG6ufT86AYpmas/UMBnyPx9X3M85AEpkRcx3B4NjD 99dTY39AmfDx0LYGDLYmIwTv50+Db0OhmXo6BlG98xP8qxSIpnp7/VcqBk8M mSqnByngnV1r+DgZgzdOtTndNRQI9jp+ZE88Bnd01AnMURT4S8sVJnsfAzev NkN6cQpsqMfShfqh7+sHXvht8x3Err9VprPCoFqy9YnLz0mQlThsTrTAYOJX 8Tup7kmwtnWndbyAQblmfh9z+SR8U2vqHzfBQFHI00suchI4tjzM2QwwONv6 mpUgNQlZ/0amXTQwkCWU1oV7T4D2Yof1AhmDvvdfHDVsJiBSsKLDBzDgfmxg LqA9AZsclb7xqhgsXzvvISE4AULML+cYFTF4rSETYBI9DmZDu+a+SmFwJqEH jpLGoEuI59dTSQya/sgc0uEag3M6S1Y+EhjU7TLKeTw3CuodN4IOHcKAJ0rj COXxKLCOqXytPYBBOmO09K7tEXCQ4/pRzo/B16viNxQ+D0P1p36Ptn0Y9K6o CuQ+HYYQgb8rk3wYbPD55GoFDsMlosgnXl4MHlYa24sRh4HObaa9lBMDqx+N oJA9BEVRpQWZLOh5xYPdt+4Owt+WkTdLzBiM3xS58/jyICg3MB08hUyX9ubM jOYgcBY0yf5jwqA7YECMgWoQVi0qRO8yYpCQeV3QPGAAThcKtiwzYGCqEJc3 bDkAESUXc+2QeZ30ze6pDkDpW8t5LXoMlNttdO23+iHPaoJPjRYDyXum0RyB /dDYzTxcR4PBAAO39g/rfqCRbMjVRi4SP+IzBciseaftd6H51UrRsaLuBx4X Ac4yKgxcKnt+ESP6QKHOJ+YscrxYLRg490ENM8OPZQIGJEPMKPZMH8jx5Aoo I4P/XP99jj7ILinCZrFtkD+y7nMu4yuwR6Z3pCGnZQ+15N7+CkRXD2Nj5JEt egnhy19hkE/PrGF7G6oO0yrelvoKboGxXSHI//HzhzmxfQX+ybczGsjB/Q7c N1d7ISoofLRlaxumXHA92qpeKJfIK36E3HXA/1FIVi90lcSxWSHftIuxEQ3v hRilNxb/NrehUaqnu9egF9JzLEmtyPrJ8vu+E3vhSnt58hNky1PRklz7egGX Dc4yQP4s5v/7O6UHFEcsT0ki75HXVA9u6YEtkUEDRuQUDZtMeN0Du97LfJjd 2IaLao4j+xN7gOrC44A25POcaw3i/j1QUGGaXIzs8i5TWt++B0qS0mhSkOM4 CJQkrR5of/a8KgS5kqfwwy6ZHniTWlLthjxUqhoUy9UD3LLr1FbIYwPatOpb 3ZAv/ObOGeQPns4CHN+74YCQkAYZ2drjeAJNSzccnL1+TB5ZZEmXzFvcDTk3 RU2kduqTE17US+6GPjfWp2LIBYWCt7KDumFyYB/ffuR0pZky3ivdsNAk9UYI +dtL4YBX+t3wTm3GdscvTh7xpFfqBi9iPEUY+WGdkvut/d1w/c6I8gHkTZEX JkxM3UC929X2ELKZ/RKhbLULXB8vGckgs4bdMAwc6wLCXu49SsgxYfn/2TV3 AYNO+H0NZFX7FRObki7o4vvdpo8czl/X7JvWBfkW/9oskfteBl4oCu+C4Zmz 91yQE/YlT2+5d0Fpav5mAPJRq5v6Vyy6IFgn90AsMpt3zLW5k10Q0/VnKwc5 01bzUNTRLjjIeCKsEllHiOb8Kf4uIC7cf/AbOYnxwkPGpU4gG47u2Y3Gl43Y cJ5jpBOYmkYkDiKfkZhnkW/qBDaLBBUH5OrrIo1N6Z1Akcg9eA+5+dOuUMWI Tsj35nz+Apk8aJxf69UJBSVDxn+Rb8VzFwnpdYLTP+Gbwmh+lt7K01tR7AS5 wWBxbWRNxuGBiQOdkCV4mCkL2bg4M3TPegeEtQsW2qP5P/1fkPpv8w6gWdau SET2nyFOCBM7QPi/D8ptyF04JeQ2cwcs2a0GqqD1Rc59ONtT2w4RXjNtEvg2 LF1M73p5uB0c2RVZnJBVtIvEzGnawefIYl4Bsukd97xj41/gZ7b8uAxaz3fC XA3cE75ASQQPro3Wf9TRz+8Zab7AA9X6ijhkXutNHpGJNpD5Tl0xhnz3R0qn fWUbqG4q+/hSY5CZ7+Ls4t0Gftu3U8tRvvSOEzIjZ1thnMh34wYdykPGtION gy0wnmvLNoLcsTxVVvW2BYro5dbUUZ5JuSSkTsW2wApspbKjvCusyTJq0GkB jmPLSzUoHy3fDdhUVX+GVd5dwqYoT7Xtm+nOv2oGGKGwtCM/v/nDUj6mGajI j/hPozw2PczIRXZtBq/yl8GqrChv45IaByWboU8+XIbIjvLwUtk8z4smuCDg 2naOC4NU9w8a0cWNIOgtpjOKXNn+/Sd3XCP4lYqWO3BjsPJF0P6zVyNEvjd1 8OfBoH1p1+BzpUYgiirklKB+EcE2lXfiYwOovSU+1xLCoCHpGmfnSD0EGudI M6F+9B7PP90r/QlOG55MzEY20XB0aOb6BPTHFB4pH8ZgpjExbmj7I1Qndqu6 oH42c73C16z9I1CJp0v1of5XnW0i+879IyhRiYl/ksVAM8ALGyqvA/apK4p/ VVD/czQ/PHyxFo5yvGfOQP1UkCrOT8+gFoZqhU+fVEO/16kL7leuhdWic6Px JPR/tAUeUOaohfiWITcldZT3c4tilmE1MG7mzvLwFAZHLqc5upypBoq/1IKv EQatspuu69SVkFPjrCJujObHJXuR0IkK0OKTqetBvqYpwKNUXQHd+c1eMufQ 90LK14T9KqCkerfVrCnq95KLdyZXyiHxaLiJgyUGxu9oDQgLHyDMiDsj8AoG YvIM2GXq93A2WkhF1hGDQw6Ms4OUMjDXbV75juzQus3r2VQGVYwupdpOGCRL xUSzRJfB2+LpC9yuqH7hheJlvjIg1czdeuOJQXDwnpPqyu/gM0M993oABuTl zsjxuFKwa/iwVRGIQRADZf2ibyk8WpuZDgpC/S1wnZbZqhQ2XpnW099G/b7n nVybeCl4G4hG8oRhYEcMOfOv4g2UOBuGKERiYFbLMvJ9rgQm+hV4XBMx8A1q rGu6UgwG04abMkkYhDVJsocbFoNka3jrMvKBEXbbi8eL4diwt7RvCgbWg7sN /ZiK4cfVV99vp2FAPHThI2fxawi6Txf5MBvVl5ltMED1GtSuts0nvsTgxfAe 6SMeRUCxT7LRfoXBYBWf0nW9IqDfK/R6E3mbsXVt6mARcH568sumGO2/jpdl nh0vhLmnqrXipRg8MMP3axsWgset0IiiDxh09oofclF+Aec2bAzT69F+S8iD VfpIPhxSFaLooP1n9W6LwRqWfFB456e7jtzAyN9wcyEPdNvr4oybMCg4LaZo X5wHTvPuVLQtGMivpq7jCnkgbeuyx64DrY+soyWa2s9B7Qq14uogBqXrVu/K 7+WAiaRjQ/4QGs/6+6eSnHPgHZckt80wBs6jrsqP9XPghdCz7Wa0H34Ry+zN y5UDZTqXR1LG0XxWWdL99vQZ8JoqpMhMoeeNN2XDmp8CFZ+F7eFFDNQ8Vyoz pbKhsM5XQY8WB/Zy248zhRmgsfUxZx5ZNb7AQDgsA6iijNpj6ND+vqGCOsoi A6ZUpnU66XFYiFRppGPKgImepAWD3Th8OEFR8HNJB6UU5151VhxCLt6wFTie BtNrHjcWeHGIYDxY4Pw3Bcod5N2vSeLwa2oo/dlGAqi00bH8Qd5s4x2yGk8A tkulzn5SOARn/mxQqk+A+Ow8hzBpHDR9mWnOxiSAcGiCRYIMDvKiJAKXaAKs 4i0nXxzD4ZuK4d8ik3jQKZ1Xe66Cg6t6W49k5yNwTLHcntDBYXcOK4PGvocg iiLbVheHhjtxxDiah0DW/Co4gZyQJy+2a+wBDFOM+cb0cNAZtIh0uvcAzt9W fdqnj0Nqp9+lmfEY0FSbYi03RvUv+cpbpETDa0vjOh1zHCxt2N2YifchPlaC IdkRB4YGl59HN8KhdcozH0MuK/kmqDMaDuZBwHoZnZ8Gv9Vk3K0NB4aDZYdk ndD7/2QNu90NB3KzRUKjM6rnbHb4LHc4yBmYXpl2Q/VfDmq8qnoH0s4v+m94 4XDDj47rSmYoGFVbc90MRvWsHt0d+SkYnBT/ZEQk4tD1h0I07L4BOgyx0U15 OGwI6vY40HtAYYD8rEgZDvG/XBVppx3BNEbysVQ9DsNbg7PC5XYQJfPqsEk7 DtMWiolTnRdgbbz3S1EfDl9EaYq5fxqDYGPfI+IYDnKf712hwXTgmd7fs7QU HCYCmoeHSzTBNnU7/Tg6XwrR3igzI6hCxD7rBcd5HBxl+Aoe0hGh/6zDRuYi Gq9LKfVjutLwdUnFP3gFB+Y2dc26MVF4ZP6EtvQPDtRqF/bVXhWC094+zAF/ cdhadRd11uMGK0a3LM5/OOTQGsk4DbDCxSB1F70NHEYf3c87oEEPl3tzZOw2 cejuyzyvfJ8AEy2nzhK3cHD43WRWzrFO6pcepYwhu3Ha/Qx+skTax0Z3yWcb B16Sz/69+2dJ3vrWv2eR8TI3N62z30hB75cPGGI4tN498uEN/RDp5uWXgVnI DJJuoZqp3SSCDzlqHJk5XS9WVq6V1BF5KpQbnbeldPkC9lp+IqmPVZmTkakx 6bfxMpUk9pAWPnvkd2sLho65pSQWt3nGYGSCmeszultFJC5Bq75EZCv+qfKk 8BzS+QgLuSTk+XH6A+6OOaSa54wxOybL7I/31MkhfRb1OZGMHCJ+L3qVJYfk eCK5KAW5I9Ty01TKMxJDvrpHGvJeLx65E2VPSSJpczVZyJwx9WP3WLJJf/gc OLKRs25a0BD/ZJEcfJMu7Vi3JO8l9UgWibX1P4anyBcCKkYZC7JIpOvfdJ8h l6XxVpafziJRpFQac5Fr2e2lgiIySVq6BpzPkXlU7R6c8cwk7d8nbL/jnwEu eaoWmSTRquWtHTuVb2n5S2eSjta7y+Qjm3qWlq7nPiEtsV+9tWO9EBGGJL8n pL3rQk07Tr2/sX5d/wnJ9Xa9VQEyw7WnujNrGaTsjNK8HX+saPoX2JpBkta6 uLJj6h80Y8aZGSTmik61F8hY/p2Mi94ZJCBu393xTJXX5GudDNL/AFGWCjk= "]]}}, Axes->True, AxesLabel->{ FormBox["\"N\"", TraditionalForm], FormBox["\"P\"", TraditionalForm]}, AxesOrigin->{0, 0}, Method->{}, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{3.6623077844093037`*^9, 3.6623089822885103`*^9, 3.6623466933727055`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"u3", "=", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"f", "[", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "]"}], "\[Equal]", RowBox[{ RowBox[{"n", "'"}], "[", "t", "]"}]}], "&&", RowBox[{ RowBox[{"g", "[", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "]"}], "\[Equal]", RowBox[{ RowBox[{"p", "'"}], "[", "t", "]"}]}], "&&", RowBox[{ RowBox[{"n", "[", "0", "]"}], "\[Equal]", "5"}], "&&", RowBox[{ RowBox[{"p", "[", "0", "]"}], "\[Equal]", "6"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "10"}], "}"}]}], "]"}]}], ";"}], "\n", RowBox[{"plot3", "=", RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"n", "[", "t", "]"}], ",", RowBox[{"p", "[", "t", "]"}]}], "}"}], "/.", "u3"}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotStyle", "\[Rule]", "Green"}], ",", RowBox[{"AxesOrigin", "\[Rule]", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]}]}], "Input", CellChangeTimes->{{3.6622600160741262`*^9, 3.662260043356512*^9}, { 3.6622600965462265`*^9, 3.662260111749984*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {RGBColor[0, 1, 0], LineBox[CompressedData[" 1:eJwl13k8VPv/B/CJkoS41uIiJUm6JcnWeR97lq8KJYkiS5souyIJFbJliXDt FNn3naLsIjQlEspeZIkr5/f2+M0/5/F8zDxmHnPmPa/367PTwk7fioFGo0lu oNHWr///4Cb//8pP8sV92v1nhIscHaXLsgzwkXQWIlWvmYtU69ObO17JRzoZ nqwci+AiLc90PLNw4yNLhzgLOw9ykYL0nLXVBV7S/46bs6bjX2TTYZ/z3r95 yFLz73Ib9nGSOmePt4eJcJPvnhEh4+rspLpxv1nVFAdpy6yZPS/OTtJdfUpD ujnIt0G1T7RZ2El5DoHAwHIO8pHodEZXBxvpQjJ6rz7kIFvEhTTkzNhIPqYH Q0XiHORWvhDuxw9YyeT46IiUD+wk12KA2SumrWQs99PRHhFWUsGn5tulcGby oGN9UseNzSTL0sKvtUubSC7euZNOdTRSONn1APcFRpKzakTzt/JvmGQPdc+Z 3UAqnzn78LfELCj52whncG0gZbhrfpfMjIG0p1CuqyuNdG8qqXXIHALeb9Kp 37bTyNF2w9r7x+jA+6XteB8/jRyXmDg99zcdKouZfjXx0Ui6e0/hw7UPEB58 8UQRD40U1LvGvL/2A4wyCbxP5qSRD7/XxmiqfwDpN5/sP2+hkfEnPdjSz/RB y5YDTqZLFOwy/seoOLwHJL5tEixaoODkwoR6rVsP+KT8JcAxT0GY4Sr/lFkP GJ5yZe38SYHCZb+yDIkeMMty2+MyQcGdjzyrubXvYZPS8JjpAAVKbSGy9Plu OKxwmc32LQWsb1usHR27IJV/rY/lDQWfeI4x3jbpAsaXJz5nNlDwv6mtD5NV umDiz3nvpXoKIsMjQ4w5u8AwPzqjsIqCJTLts2HuOzg8YrBcV0BBj+JlW4v5 TqgQHT21KYkC2cjuZAPxDmAbv55AS6QgPjhRTvpPO5zOPxyw9i8FHruPLWl1 t8O5Pcq7GeIpMF6907DLqx0ueOVMisdQ8NHa0861vw3UTd1YJsIomJfzUrP8 txUkuP6q2edHQYIknxGh2ww/1mjxHr4UiAS+prNJNoMd28lTXT7on8Pmm1ma 4eeL7RL37lOQE9+b7fK2CfaFZWjNe1EwHS14S1OzCY5dEs2TukNBrXiBvpPu W5AwvGgXe5uCvx56XWiVegvcTfu6WNH9Jkd3aW97C0nmpPucGwUxem7MZV1v 4IvCFrZ3LhRoZNuqXTB5A3Y1MQx0Bwp46iUtUh0aQbRwV/dF9B9ehW36Ro3A oLtHeOIWBTa7JUNEFRvhatBl4Q3o76uaZw4wNkKSR5gbaU+BcP6NH5PhDTB7 I/Acgy0FzWW9x/qqX0OB6s7r3jb4+toZYzXJV8Dcx3pPFr33kZR8CNcrsL5l WDFpTYG/f7/j8n/10HCvNcoYPaWWdm1XWz0MaxwqUbGiIGI69dg7+3qwMYjp OH6Jgntfi445VtXBkjWrDjta4ydLnk96HXzeLt/23gJ/n7fS2rmhdcDd0zlg ibaQ+3rtrHUdsI2aMYWaU/C+mmtgjKMOJP2Fv/JdxHl6ZsY8c7UWroVO/566 QEF95p/oxDO1kMaTu1KP/riFTeuGSi04sO4svYlO4rT00N9RC1v8hSboZhQw NZw3942sAYEr8nuL0QwvSzVc7GqAY+Gb6hO0bMznG9HHa8C1j4f9JFrNICTV 9r9q+C3i+7rbFO/P2LLniUvVMFK31FCMDkte0606Vg1GUTLRMWj7DWPRxvzV kJK8N8cSXefk3C7YXgU2ldMz2uh8B1F11edV4N32dOUQ+v1w7dkonyqIjK20 Y0CnjH91fKNYBc5Kqr2T5ynotLZlTebD1z9tYehF7xP7bZb5qxLGj/9Jz0Jb yAgaKGdVQtlo2rIFukOd0rojXAkjUr+YTqEjitgmXy9XgLqL4Q9A16tsFCDf V8BARLuWCFq+f5qp7VEFcOpylXKitRXJgwOWFaBBsa4womu5nrSKkBVwy+rL 3IQJ5sW7NBv5pXKoj41JG0QnMglNsneXQwu9WbwH/e40wyR3TjlUmA05tqDn vmVL6ASUQ7WtXmA9Wvyr55U8m3Jg1PK+Xo4Ot2u7rqlWDsXS01wFaO2ShQXW neXAZEt5ZaFth/TfbFgrAyEFifw0tDAvmSz2qQwO9H9MTUS7efDrupaWgUWE z7k49BM46rMcUQbf0yPbo9EhPktszx3KYOr0PVoUOsyxMNPvVBnEDRXOhKPz jjYJh/1TBnsfJ0Y9QTMthuxvYSuD8piS5TB0QZ91+KGpUrina8O1/nz/xrTt Dc2lkDkiMrzuqNTnnr7PS8Ey1dAmAk0NtfreelgK9M5b8eufJ/P16myATSko PJ/0i0GbtA/cf6dRCvn2/wjHo33b71Mqe0rB7kq2VRK6j6Voz5dNpfBvz4ez 6eibmW0VGaMlYL8ktLR+Py5/2HsvtqEE2DhnifX7NVC2U74itQTSLGsOrN/P RReutI1+JWAjs/K6Dl2vYOzval0CHvWctGa09T69DF7NEkjIdxnoQjP6uNYP iJdA3mKLWT86sEcysZO5BC7RlMhZtECkxsDBlmK4fLwzfhXNOyTQE59VDG3V mjHMOB9uuTV1R4KK4b7iOwtR9K1wvZefTxXD0dcmUgfRKz7pajOHi4HbqzyY WJ/nvBcM4rzFwBk5ymu6Pr+uAbs4PhVB1K198rZojpleodqqImB/IDPjgf5l lHEzKqEIYs4/2pqIPlFbqldhXQRcCbo3C9ClMVY3N2sXgaZIo2UjGnY6CrpL FUHap9Yf0+ioiVClrvlCkI3u8ln/fxlt2aZd8qEQjj+9m8Rnup7vTRz1lYVQ e6H2lio60alrRdO3EByPOKomorsGj0Rt4y+EXw+X9ErR8kLOGuNrBeBNL33b ge4Q47n8dbQAVq7SGWiYF12se89JFxaAndVRJyu0+1tWWzX9AjCvL+29iw78 2+Qgj0IB3Facjo9BK9+mJDeKFoDTU+GL79CWJp8Ipbl8iI92D1LF/DJa6Z3n CM+HGQcrdnO0ypfW2I47+cAQdWnGE+08omCRaZUPNW1aLRXoIH2O0rKj+ZAT HTQkj3mpzvk0T+pzHpwO9GzUwDzd6dIzaSCVB6PB5MgVtJ2f7oduvjy4caTX 8DHaaPBu1g2GPCi+s1+yB13lmuU535cLxNPTEZcxn+siuKeUfHJh8+jHnDjM c+0dHL4ar3LweYXYBnSks8HN+89yQPrX/Y5pdEToDcE5hxwwIvczgyXuZ4dz dZfEcmA6CnJG0K0L/2sI9c+GAeI9KOE+GbramjNi+hK2KmTRrqP//Bf/hE32 JVyO0WWORY+5bXxwnf0lHFXzHVtFbzZNtm2pyYIaPameOtxXVNrM7EaxLGAr EEw1ukLBb4PJS2LLLyCk38UuAF1kMGwV+P4FVJnyONagz1e/oonlvgClLTYS e69SsJ3Lj2HC5gW8dwg7tIpOuckClfTn0LzNaWf2dQpOVQ0OazVmgFWhNoyi +Rt7YrJSMkBVPjFQEPdpg0zPD6X7GTDtK1IQgE7ylnMaJTOAMSZC8PoNzNMo /0W96nS498ajVQb3cU8bS5huXRroS39KGsJ9/iB0UtDmWwr84tO7IuhIQbvS R/bg5hTwcS7RMULbq7EI9GengMrINYs2dI2Ua8mISwr0XD3RVO5EwfWWYKcX W1NAJuIMWwz2h+6tsV8+ySdDkBeTrQ32DRFRhqtPcxIhOf10Rwo69JjR881P E3GftcFXtO4nmVORXomg9zldyxT7S3cvw0FO/US4xsa2aOBBQayZgpfrYgJU EdvOqd7FfRT3ee+YWgK83JM+KY59yPmk6KTzTBxs4dohaYGGb2Y8Kk1xwNno aRuLVjt7/75iShzor4qucGCf4trZoFJ6Lg7a2f9IrqBDnBZ+dDXFguvCvopW 7GN7nusLnMt9BoNBFxbt/TFPq5IyDsRFQ7NHgGgmmuu5stYZj2gwEO7XHkVz 5w36pZpGA3/BoWDjAApOM1fzlQtFg3hm9JByIPYnFz+N4qSncF6nzIczCPuo vUlgZ14U9Do/9s4MpUD65w57pckIAJUnheNoGXEJjey2COjIqf4kjn3R75Xq hGZuBPy2G2ROQQe5X+yadYrAawn92RMKrm5+GLODMQLir8gfehSBednI0fZk dzi471Z9YhyN83wlvKPeOww8VvZsj0QHN9e5tV4Jg2sJ3MFdaJ1XMXlLJ8Pg 9rtYbR3sq+rtXrvzhcMgc033j+IzCh7ecw7Krw4F3qNBcjviMA/4uqSqGELh eXaiclMCBQvx/wxlqwaDtqxiLoUe7TAw0xcMhgrJATZZ7MvaSkEnxBeCoLt/ JCIJDXPxXpbpQcBtH9Xrjv1a4MHw2G72IKDPbGTbm4J9qjKgImAkEEyPFY07 plPwTeS+/40Cf0j4tcmk5yX2QyOPsJg2P5Ad7yW2ZlPw1rWDxTPbD+RWFliU 0SMKNCog2A/IxEWTLHQqYeu4R98P0q0nB+/lULApylv9BN0XuMenrffmYX8Q 2cRJ/PCBjZujpS8VUuCoTS/aLHcfrtrOVwaVU/Bl0fVcjLQXiL0XSahCf/gz tfuboBf0Sihfm0JvmnmzqrfZC1SZzcu0KiiQK9rlM1N6F26dP3KEsRL3vbSo shLHXThTMZN5E88bWYlSMtpNHjAgFPVMqZaCwYC/Ww9cug07LLJW/fG8wtDY 264g7gKTuSL789AKTRuSNVlcYO3ZYc0+tGjhkWeu086wTVOF3NVIgQvPYxmN QmeYXTQnytHM3fr1/qrOEMrbdmMEz0MnlPK0wi87Yc9PfyXRTIHr0JXxkBYH kN949rxbO75fATn7aMoeGrk+WMWhmQzOHn/aYw9vRn6erUO/mqqqb6i2x/7G usrcgfNdauzuEWoPZ2qaZaPQFsail0zk7EHkwRnfnE6c950fdxjz2UHI4KGa ji7MN35CfWvwdRimTwV19lKwkZZyyof/Mrj/imh0/Iz54KB2XCzAHGL9U98w DOP3Cd3v5F1oDPF3tLZtH8N9ZVpbIGykD4f1+ou5p3A+H2wX9nutDVuWPR/n /MD8Z1j8LMGkCvuGCzji5ijIVrEazzuiCCw/6858xfOlyrKgJ+f3w/BVf+Lj 1CL+XxxGRcVM9oOkBnPR3d8U6H+fJwSe74aL/6kKvV2mQPKLdFeSjhD0EsXn Z1ZwHrIDpUYTeSAr5KZF53+Yr/zKfEeit0F8cW5l9CoFu2PkBefdmODjz3O9 h/9g3ps3pgufo4HoFnpGLrqxUd1o++wSoVdg0yK8huc/ne1fprBLVW2orXBE c2dnLtaMjhHOG+YYa9Fyzu5ka/YQwcwhy7KKNhZ1FdPRoBNi8yHDEhQFLFd/ 5ha6dREJywGP9dEv/rYNk9VrJg5UDvvfRL8X/mfrI/FXhGH4cLA/+to+1dfZ nJWEuV5GYwL6g6qV1InNhYRT39OiPLSlXPw9afmXBL/t/PK6E1js+g5xvCS4 8rmJfLSFhy5c/Z5FCDCmNKzb/ki+om9kFpHcydBVgA5/1JJyfimT2P9kfLAI PfdYW8zo1Qtizvvfd2XoYGuR4y+8M4gjyRPs5ejYAxOaOhczCBZFmu66GUXH 2P4mMggX/4CGdc/c3jR8aiWdeFAiXlyBXo24bLfsmE4Iv45/XIX+dWD0zyaH NOIma/qbde+Y91ULN0gjHHLvbKhGM724IXlCJo0Iex3iuG5lemyn1mIqYb3f /GwNeusgu6zOnVTC3pwesm6dV6FKR81SCXlLkaZ1b7pt3fk/MpXgCBSQr0Uz nPGPXN6YSiSxddqve3ZWQC3oewqxwmOYse4SfR8n3eYUwqQ7fXDdUYWWY4df phBMji28deiPBmbn1EJSiP8DwxpmGQ== "]]}}, Axes->True, AxesLabel->{ FormBox["\"N\"", TraditionalForm], FormBox["\"P\"", TraditionalForm]}, AxesOrigin->{0, 0}, Method->{}, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{3.662307784441306*^9, 3.662308985252516*^9, 3.6623466950758915`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Show", "[", RowBox[{"plot1", ",", "plot2", ",", "plot3"}], "]"}]], "Input", CellChangeTimes->{{3.66226004852859*^9, 3.662260062888573*^9}}], Cell[BoxData[ GraphicsBox[{{{}, {}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJw10wk0llsXB3BSZso8NFERKlOiVM9fXZQ0UaJQV5nSDbcobopMicxFGsWX RDLPF5mnMs9DMmd+TK/XkPd7Wt/6zlpn7fVbZ52z9z5nHcmrdvoWa5iYmMap +Tv+b5D4f3TzJNNYqKi8gfOKZccUlvZZF/NSTlRGKz1tCvKvtaUlKbskdelk Bk5ha9hkkzplg+G9Hu9spqAul1pmTLk0W+1MptYU5LjEZj0or+1cd48uMYWR pGy9VMoWJfubzFcmYR8q3zFC+fCUjcxK6yRy5Pg8dzKT+NGkqpWfOonCySXt vyj/Z1KVHhc4CVdDL/Esyp3p69YX3ZjEZJcOjXMNia7ow4Ysxychm9lfb055 WcHrje2OSdzUEX1fSjns4aNUFuZJXDPl5n/FQuJChIZXXM4E9F/Ev+RbSyI6 W7s3N3wC3HeiV/wpLzm91qE5TOCSm8mOl+tIiD/uvD+oMAE5m18du1hJsKnw j0TwTOCFfvbxYsr2nXpv74yN47m5rBwrO4nbzYeVYj+M43bRuYBkysqaXYkr XuN462Lre42DxPcvvflO5uPY8bfZrk5OEjpyrE1DkuP4Y+mAmigvCX8fm/Jn b8ZgkGPvvkCZVLbNlnwwhk4rE5nu9STUgl2+NZqOgVFw1TKXj7o/zYrYj5vH 4JBc3V4kRELo+NfjIm9HMZqZIdskTCL/8UubWtdRXA2UixgTITEkvuPUpz9H cbijNnu3OIm69fqxjdtGUWNSo7awhcQ5h3PMTbEjkNgVl71fgoSiSM6tBN8R +Cq/knSTJHH/ZuzpuL9GIHjhnI/EDmq96mY0j9II+BqYpmNkSYSYtJy6k/sT SlsFFEr2kTh7rW7Dp5ZhRNFkGjzUSIjlf7Y/kzWMVZ9H/ToHqHzbjt8VezGM L/nqiiOHSFwris+UuDwMs6BDfrc1Sai7qeTThoewzcw4x0KbRIbWCHdV1RCu JCwJXT5OQtPPyK0oYQhBz1uUzE5S/elZCm5zGEK3g4hI0nkSBdwPU8LWDEGg V7Os4QKJQG3eKf+hQZywHTRbNiKxPl+xI7ZqEHuUnuCyKYlIbRq7Tugg1qMs 97olCdPeyt490oOg1/LTgpxJjDZLXruqPwDl+ae1vC4k/lE6HOW6fwDDMRkb Qx6Q8Clyrc/bMoC/68MnYz1ItAWNX3w11o8Bea4U4QASSooent3e/Shtbz07 Hk2d91CL/WRxH8ruqY7nxZD4V2Fq0jy+D6UuNo+efiTxRD3l0KvQPsyEPH13 NpFE/5eKWxbmfXjQkB/Fkksifq0w72W2PkjGZDaebqTec2C7f5l+L6zTBHfu byHBL5UYKkv0wucNk5NUO9Uv63mB97K9MBbi+MXVQ/2XfybYB5l6YU5z+sU2 RqJk8NYLr6QfcBKY2J3JMo1/nXpXFQR/oCZTpaObdRqRI7t5eZh/QNRAUImd cxpnXVRimLt64F9xutxqwzS0nw5IGQX1YCotnE1/8zRMxu6tbFr+DvvUFMsa tWmsTR/WaG3rxjknv5N7Dk6DVV6R9Ux6N64WbvYLJKZRFsQ0SAZ3g/uiGcNU axqVurIKKbrdoJWzYNu5aVgd4kuXKuzC9anPU3/YTWPNbtI9JrUTGw8x91V9 nEaCIfPTwvR27DjiVu+UQNWTcbQvO7wdnQ2frWWTp3G95qVAs3M7js3tuh+S NY3FviWX20Q7ysK2VniUT2MiSoWuW9kGV25F5Z7BadzwZmY/PtiKKYnwNyY7 ZnBQrsf5z30tcMk3cTaUmYGsndmJ6xtbMOva5HR+9wxoudYHgphbYFzZ1nxe ZQZufSs/1GqaUVp3PMJWcwbdultvjlo3IyZHd2qNxQyOfH1nWRDdBDY+Q6On H2ZQz/nm0R/yjZA2zF7a+WkGKVGlUiNCjdR7cD3NS5rBP/kK1xJ+NUD1tHLE ZPYM4mxcpIK/NSDQ2uum1dcZqMx9iy+0bcA9wbHDSdMzyPqy9vv7jHr4B7rQ HhyeRd1EqeE94zr83GCScfzoLMRCQ/9N0K7DkUup3wWOzUKNy1RnSakOAWwP DT+fnYXFm4Fzvex12NzkbD97bRYsFm/nyuxqIfzR40mO7yxWD40/VNtXg0q9 EimJ9lmUsTOVCA1UY++rx29yumdR7Hi0/2dRNebXXe8x6JtFYdWv0b531dji c+VTwNgsyMDHMyf+rEakhpYYx+oszh/9UTf4vQo7RjZFbNk+B1FjmR7J/krU 7nqklnlzDpY/HkwGsFbg2GH/cvNbc3B5Ipo2NlKO0O+V+fx353BjvZmgzbdy 7AkbbbFzm8NI0/yvqqflaPIdMZEPnUOfkfdeMalysEPIJCdrDhqOhx3Kdctw 38h96zLLPDTOzrvaJpXgiGHGFiGOeVxJcXCOeVaCCa0cBQXeeUgM2fkw3SvB vXhr52ui8/gZxqokrl2C9vvX9b7unkd1k5hiT3cxnrYrmLwymEdIwX8E/QWK IdrkuU3iwzy2TLfRzMIKITOpc1T10zwy+IROBrgW4luN6oaTyfO4pB+R02pd iOdTvvF3cufR3R9xsfBgIW4xK4eW187joejFjrG+L9hPlyowoM/j/Kn8PFfV L2j+OXt2gw4NLJ8yyq715+GTv6094xQN1e4K75Xz8rB1sHxiQp+GCeutd5TC 83Beln2xwoQG48/befJ182DleJH/rj0NWbsWe7gz/0VwIL9BcjgNXZeTXpwJ ywXXbNjJgEEa5HZmP/numA2u5JBq81Ea8q7WlxIG2VhXffCq+hQNz4pdBStU snH3RFtNH52G7tjT8gZzWdizwmEnw70A23H3+XOOWajR+yrmpbyADZ/SfmQ9 yETrdHrMnQcLkLI72FuVkI73HXGWne4LMKn06PgWmg4ZPR1ZPFqA9C8Oxynn dBSnGiSzBC0gyrZ/bYB2Om4N2cW6vVvApUH9epXeNHDllm3QKVnAlLuVLNem NJy5HPOFk4MOtrTNiWMxKaCla6nwB9Lhd8907QfOJHActOvzDqXj0BHjTRZj iVjV0+dfCqfj7I7gmeTCRFiF/DXbGUlH64PJkTHbRHANr430T6HjHnupeEf1 ZzjJm1V/aKbj/iN/NevABJR8iktMEl+E7er4TNDBeOg/s5sdeLuIjPaE5DUb PwCD2+U+Ry8iPG/Y9/NqDCrWRA45fliEpvQ5H5e+GEy8WT/FlLgILodsnQdx MUgMi1dZl7+Idse0esFDMfin+r1uWeciVnieWd20eA89x2VbGeElpLuXyFfU RmPfvB6zqfcSpIQ/+R1djoTTmIV62uMltIzHtxUORUL3BBY5/JcQ5DYcfLEh EpYCFWzJoUt45dlWX/8xEl8CO8wnIpcQ6bVBq+9iJGS6ljm35i6hwa5Wt9Hl LU75yG63nFxCrcMdIkfxNSLSHk95nV3GEl9XSrpgBEZZAjUKzi2DcSm4K2f2 OfaSR9poF5bx5H7vyGjDc3T88Or603QZzQIBjVXBz9E2eomQsFlG2EDODw++ 5zgw0PPspMcyLATu1MaJhgPWzqdN05aRKj+WY6z5DLnqLv1/861gf8EVDV62 EKw7eUF5veAKUghh3XYyGEMXLgrEC6/gX5UWq4KOYCRpXPb/vnEFvSvZxl2f gyGSuXpDRXoFrcfWVRsYBYOv1EHmlfoK9m46lbkrKQimgpxal6+uoC7L+pHw YACUxViSixNWUMKTn+V51xeaSX93nMYvvDpxo8tlxB0L+9hCjLJ+4X1b5evW XfcQLKO0RIqsYmGto9/2mdsY7Hflk7VbxfOfNiH97n9hXqzg297UVXhbzEWp NJlD7O38a09yFRvqfooIRJlie+STNeLbGPjH11Jweq8BDK0PuFkcZ2AjvTiR i/UMNKyHMj7aMCBYxNy3TlwbjPCIBronA2Lrjyk0imlAsDpf0+AFA9Enmcc3 vlCDtJZL0bUEBo65vr9e2aaI1zVftyzmMvDSP77sznMZMKr9qkYqGGirDnCQ dZHEwNHigUONDByQrhDwZhHDizIdT4lOBirmr255eZIf5tNfQiT6GKgu08jR FuCE34KexZ1hBjRTlzP1mVhQlPlZsnSMgZ2zFar+3csEd1a95/MpBv6yeswv MzRLbGbRXHKfofKvfKX/yTdBXKiJthSZZ6Bb4uuN8wkDhLeKWgHPAuX07W7u wt+JuyJp/lF0Bkgnro5y1hYi2XxOi2OJAU77dZfCrWsJ+oz6CfFlqj76zomw 4TLCgsfFlGuFgSfyMwmuml8Im51sk1WUC5iDNllpZBJG+rwtJr8Y2BybE7yb kUS09FcOdlNeP3vjytN9sYShWjS3xioDfEW/No2+eUecCiyWCKSs+s5LwfZb BOEpzb2/mbL5KWXWU5YhRIydejAng6rH2S6tvs2X+LBoac1F+VYPzV8u1Zfo 1GkluCmLSg8oZfn7Euyc3iM8lEsYXT72f/gSrbx7VPko7wlpkz2T/JhoX9ie IEL57da5635hPoT+t69COyiLqMg1K3p5EzZXXrT8dlDmsc4oC29C4l1+mBRl ZULy+hFtb4L+mEdoJ+U1J2wFWNi9ib/PNHPIUbbjU7cM9vci/ngR2KRA2YJz aFtkpCeRpsvrp0j5tmtGVK6HJyHKNqGh9Hv/t45HDEtPQm/ma5wy5awhT2fG Hk/iFV367j7K26tk8tvyPIhCwwwZVcoCWWa7FaM8iLW2ce2/rXg9ZzLB24N4 IFx8YD9lDk4lq41nPYjVxp8/f9t+jjmCc58HofLWMfwAZeNwI+Gt4h5EMY+N ljplXnve10YMd0IvvWzmt+uXV0YzBtyJ/wKM6oR2 "]]}}, {{}, {}, {RGBColor[1, 0, 0], Dashing[{Small, Small}], LineBox[CompressedData[" 1:eJwl13c8Vf8fB/BLZjIzM/uGykh0jYz7vmhYWUWyqSQrhCQrpAglWwhFiIqU spUVsrNnXaLITDLO+X08fuef83g+Huee837cz+fzen8+++2vGV+mJhAIwlQE ws79/xcD+f93NvJFydZn+xboySu/Y60cv7KSfykV25mM0ZM9Hnx4wPyClSxg xC8gUUVPvrSZT2Q+z0qWMygR1vKnJx8VCK/uK2Yhlx6SzuEl0JNpzZqMNTyZ yV8mb7FrCdCRDWP4JzkFmMgs/e2cTI9pyG1ZjuOnqOnJHMuvAo5rUZNPFK59 xIkEMqGfNmPXDIHM6MyTr3/rL+h8dx+PZCKQlyb2v16VXIJFcsbJDAYCuTvH Su0z5xJkLz8vL6MlkD+Jcbys2l4E/Mprw384DlPJ5v60nYvwnFD+N3UWB04u v49MPovw45p3M20NDk0d1udTHyzAr/NT3/954KDgOzeySjUPEkbG1sGuOCgP 9KssDM2B3Fe/92xXcXBy9lwQKp0DmR/iLfq2OIjGvBURvDIH2yF7E0kGOPhc KoSojl/w0nBNZPwIDnMGFup/8n8CBHiNVq5icNtMLJM5dAaqk0dbUpcwOJk3 ZGR2aQbW/n1+H/QbA2nzG6ufT86AYpmas/UMBnyPx9X3M85AEpkRcx3B4NjD 99dTY39AmfDx0LYGDLYmIwTv50+Db0OhmXo6BlG98xP8qxSIpnp7/VcqBk8M mSqnByngnV1r+DgZgzdOtTndNRQI9jp+ZE88Bnd01AnMURT4S8sVJnsfAzev NkN6cQpsqMfShfqh7+sHXvht8x3Err9VprPCoFqy9YnLz0mQlThsTrTAYOJX 8Tup7kmwtnWndbyAQblmfh9z+SR8U2vqHzfBQFHI00suchI4tjzM2QwwONv6 mpUgNQlZ/0amXTQwkCWU1oV7T4D2Yof1AhmDvvdfHDVsJiBSsKLDBzDgfmxg LqA9AZsclb7xqhgsXzvvISE4AULML+cYFTF4rSETYBI9DmZDu+a+SmFwJqEH jpLGoEuI59dTSQya/sgc0uEag3M6S1Y+EhjU7TLKeTw3CuodN4IOHcKAJ0rj COXxKLCOqXytPYBBOmO09K7tEXCQ4/pRzo/B16viNxQ+D0P1p36Ptn0Y9K6o CuQ+HYYQgb8rk3wYbPD55GoFDsMlosgnXl4MHlYa24sRh4HObaa9lBMDqx+N oJA9BEVRpQWZLOh5xYPdt+4Owt+WkTdLzBiM3xS58/jyICg3MB08hUyX9ubM jOYgcBY0yf5jwqA7YECMgWoQVi0qRO8yYpCQeV3QPGAAThcKtiwzYGCqEJc3 bDkAESUXc+2QeZ30ze6pDkDpW8t5LXoMlNttdO23+iHPaoJPjRYDyXum0RyB /dDYzTxcR4PBAAO39g/rfqCRbMjVRi4SP+IzBciseaftd6H51UrRsaLuBx4X Ac4yKgxcKnt+ESP6QKHOJ+YscrxYLRg490ENM8OPZQIGJEPMKPZMH8jx5Aoo I4P/XP99jj7ILinCZrFtkD+y7nMu4yuwR6Z3pCGnZQ+15N7+CkRXD2Nj5JEt egnhy19hkE/PrGF7G6oO0yrelvoKboGxXSHI//HzhzmxfQX+ybczGsjB/Q7c N1d7ISoofLRlaxumXHA92qpeKJfIK36E3HXA/1FIVi90lcSxWSHftIuxEQ3v hRilNxb/NrehUaqnu9egF9JzLEmtyPrJ8vu+E3vhSnt58hNky1PRklz7egGX Dc4yQP4s5v/7O6UHFEcsT0ki75HXVA9u6YEtkUEDRuQUDZtMeN0Du97LfJjd 2IaLao4j+xN7gOrC44A25POcaw3i/j1QUGGaXIzs8i5TWt++B0qS0mhSkOM4 CJQkrR5of/a8KgS5kqfwwy6ZHniTWlLthjxUqhoUy9UD3LLr1FbIYwPatOpb 3ZAv/ObOGeQPns4CHN+74YCQkAYZ2drjeAJNSzccnL1+TB5ZZEmXzFvcDTk3 RU2kduqTE17US+6GPjfWp2LIBYWCt7KDumFyYB/ffuR0pZky3ivdsNAk9UYI +dtL4YBX+t3wTm3GdscvTh7xpFfqBi9iPEUY+WGdkvut/d1w/c6I8gHkTZEX JkxM3UC929X2ELKZ/RKhbLULXB8vGckgs4bdMAwc6wLCXu49SsgxYfn/2TV3 AYNO+H0NZFX7FRObki7o4vvdpo8czl/X7JvWBfkW/9oskfteBl4oCu+C4Zmz 91yQE/YlT2+5d0Fpav5mAPJRq5v6Vyy6IFgn90AsMpt3zLW5k10Q0/VnKwc5 01bzUNTRLjjIeCKsEllHiOb8Kf4uIC7cf/AbOYnxwkPGpU4gG47u2Y3Gl43Y cJ5jpBOYmkYkDiKfkZhnkW/qBDaLBBUH5OrrIo1N6Z1Akcg9eA+5+dOuUMWI Tsj35nz+Apk8aJxf69UJBSVDxn+Rb8VzFwnpdYLTP+Gbwmh+lt7K01tR7AS5 wWBxbWRNxuGBiQOdkCV4mCkL2bg4M3TPegeEtQsW2qP5P/1fkPpv8w6gWdau SET2nyFOCBM7QPi/D8ptyF04JeQ2cwcs2a0GqqD1Rc59ONtT2w4RXjNtEvg2 LF1M73p5uB0c2RVZnJBVtIvEzGnawefIYl4Bsukd97xj41/gZ7b8uAxaz3fC XA3cE75ASQQPro3Wf9TRz+8Zab7AA9X6ijhkXutNHpGJNpD5Tl0xhnz3R0qn fWUbqG4q+/hSY5CZ7+Ls4t0Gftu3U8tRvvSOEzIjZ1thnMh34wYdykPGtION gy0wnmvLNoLcsTxVVvW2BYro5dbUUZ5JuSSkTsW2wApspbKjvCusyTJq0GkB jmPLSzUoHy3fDdhUVX+GVd5dwqYoT7Xtm+nOv2oGGKGwtCM/v/nDUj6mGajI j/hPozw2PczIRXZtBq/yl8GqrChv45IaByWboU8+XIbIjvLwUtk8z4smuCDg 2naOC4NU9w8a0cWNIOgtpjOKXNn+/Sd3XCP4lYqWO3BjsPJF0P6zVyNEvjd1 8OfBoH1p1+BzpUYgiirklKB+EcE2lXfiYwOovSU+1xLCoCHpGmfnSD0EGudI M6F+9B7PP90r/QlOG55MzEY20XB0aOb6BPTHFB4pH8ZgpjExbmj7I1Qndqu6 oH42c73C16z9I1CJp0v1of5XnW0i+879IyhRiYl/ksVAM8ALGyqvA/apK4p/ VVD/czQ/PHyxFo5yvGfOQP1UkCrOT8+gFoZqhU+fVEO/16kL7leuhdWic6Px JPR/tAUeUOaohfiWITcldZT3c4tilmE1MG7mzvLwFAZHLqc5upypBoq/1IKv EQatspuu69SVkFPjrCJujObHJXuR0IkK0OKTqetBvqYpwKNUXQHd+c1eMufQ 90LK14T9KqCkerfVrCnq95KLdyZXyiHxaLiJgyUGxu9oDQgLHyDMiDsj8AoG YvIM2GXq93A2WkhF1hGDQw6Ms4OUMjDXbV75juzQus3r2VQGVYwupdpOGCRL xUSzRJfB2+LpC9yuqH7hheJlvjIg1czdeuOJQXDwnpPqyu/gM0M993oABuTl zsjxuFKwa/iwVRGIQRADZf2ibyk8WpuZDgpC/S1wnZbZqhQ2XpnW099G/b7n nVybeCl4G4hG8oRhYEcMOfOv4g2UOBuGKERiYFbLMvJ9rgQm+hV4XBMx8A1q rGu6UgwG04abMkkYhDVJsocbFoNka3jrMvKBEXbbi8eL4diwt7RvCgbWg7sN /ZiK4cfVV99vp2FAPHThI2fxawi6Txf5MBvVl5ltMED1GtSuts0nvsTgxfAe 6SMeRUCxT7LRfoXBYBWf0nW9IqDfK/R6E3mbsXVt6mARcH568sumGO2/jpdl nh0vhLmnqrXipRg8MMP3axsWgset0IiiDxh09oofclF+Aec2bAzT69F+S8iD VfpIPhxSFaLooP1n9W6LwRqWfFB456e7jtzAyN9wcyEPdNvr4oybMCg4LaZo X5wHTvPuVLQtGMivpq7jCnkgbeuyx64DrY+soyWa2s9B7Qq14uogBqXrVu/K 7+WAiaRjQ/4QGs/6+6eSnHPgHZckt80wBs6jrsqP9XPghdCz7Wa0H34Ry+zN y5UDZTqXR1LG0XxWWdL99vQZ8JoqpMhMoeeNN2XDmp8CFZ+F7eFFDNQ8Vyoz pbKhsM5XQY8WB/Zy248zhRmgsfUxZx5ZNb7AQDgsA6iijNpj6ND+vqGCOsoi A6ZUpnU66XFYiFRppGPKgImepAWD3Th8OEFR8HNJB6UU5151VhxCLt6wFTie BtNrHjcWeHGIYDxY4Pw3Bcod5N2vSeLwa2oo/dlGAqi00bH8Qd5s4x2yGk8A tkulzn5SOARn/mxQqk+A+Ow8hzBpHDR9mWnOxiSAcGiCRYIMDvKiJAKXaAKs 4i0nXxzD4ZuK4d8ik3jQKZ1Xe66Cg6t6W49k5yNwTLHcntDBYXcOK4PGvocg iiLbVheHhjtxxDiah0DW/Co4gZyQJy+2a+wBDFOM+cb0cNAZtIh0uvcAzt9W fdqnj0Nqp9+lmfEY0FSbYi03RvUv+cpbpETDa0vjOh1zHCxt2N2YifchPlaC IdkRB4YGl59HN8KhdcozH0MuK/kmqDMaDuZBwHoZnZ8Gv9Vk3K0NB4aDZYdk ndD7/2QNu90NB3KzRUKjM6rnbHb4LHc4yBmYXpl2Q/VfDmq8qnoH0s4v+m94 4XDDj47rSmYoGFVbc90MRvWsHt0d+SkYnBT/ZEQk4tD1h0I07L4BOgyx0U15 OGwI6vY40HtAYYD8rEgZDvG/XBVppx3BNEbysVQ9DsNbg7PC5XYQJfPqsEk7 DtMWiolTnRdgbbz3S1EfDl9EaYq5fxqDYGPfI+IYDnKf712hwXTgmd7fs7QU HCYCmoeHSzTBNnU7/Tg6XwrR3igzI6hCxD7rBcd5HBxl+Aoe0hGh/6zDRuYi Gq9LKfVjutLwdUnFP3gFB+Y2dc26MVF4ZP6EtvQPDtRqF/bVXhWC094+zAF/ cdhadRd11uMGK0a3LM5/OOTQGsk4DbDCxSB1F70NHEYf3c87oEEPl3tzZOw2 cejuyzyvfJ8AEy2nzhK3cHD43WRWzrFO6pcepYwhu3Ha/Qx+skTax0Z3yWcb B16Sz/69+2dJ3vrWv2eR8TI3N62z30hB75cPGGI4tN498uEN/RDp5uWXgVnI DJJuoZqp3SSCDzlqHJk5XS9WVq6V1BF5KpQbnbeldPkC9lp+IqmPVZmTkakx 6bfxMpUk9pAWPnvkd2sLho65pSQWt3nGYGSCmeszultFJC5Bq75EZCv+qfKk 8BzS+QgLuSTk+XH6A+6OOaSa54wxOybL7I/31MkhfRb1OZGMHCJ+L3qVJYfk eCK5KAW5I9Ty01TKMxJDvrpHGvJeLx65E2VPSSJpczVZyJwx9WP3WLJJf/gc OLKRs25a0BD/ZJEcfJMu7Vi3JO8l9UgWibX1P4anyBcCKkYZC7JIpOvfdJ8h l6XxVpafziJRpFQac5Fr2e2lgiIySVq6BpzPkXlU7R6c8cwk7d8nbL/jnwEu eaoWmSTRquWtHTuVb2n5S2eSjta7y+Qjm3qWlq7nPiEtsV+9tWO9EBGGJL8n pL3rQk07Tr2/sX5d/wnJ9Xa9VQEyw7WnujNrGaTsjNK8HX+saPoX2JpBkta6 uLJj6h80Y8aZGSTmik61F8hY/p2Mi94ZJCBu393xTJXX5GudDNL/AFGWCjk= "]]}}, {{}, {}, {RGBColor[0, 1, 0], LineBox[CompressedData[" 1:eJwl13k8VPv/B/CJkoS41uIiJUm6JcnWeR97lq8KJYkiS5souyIJFbJliXDt FNn3naLsIjQlEspeZIkr5/f2+M0/5/F8zDxmHnPmPa/367PTwk7fioFGo0lu oNHWr///4Cb//8pP8sV92v1nhIscHaXLsgzwkXQWIlWvmYtU69ObO17JRzoZ nqwci+AiLc90PLNw4yNLhzgLOw9ykYL0nLXVBV7S/46bs6bjX2TTYZ/z3r95 yFLz73Ib9nGSOmePt4eJcJPvnhEh4+rspLpxv1nVFAdpy6yZPS/OTtJdfUpD ujnIt0G1T7RZ2El5DoHAwHIO8pHodEZXBxvpQjJ6rz7kIFvEhTTkzNhIPqYH Q0XiHORWvhDuxw9YyeT46IiUD+wk12KA2SumrWQs99PRHhFWUsGn5tulcGby oGN9UseNzSTL0sKvtUubSC7euZNOdTRSONn1APcFRpKzakTzt/JvmGQPdc+Z 3UAqnzn78LfELCj52whncG0gZbhrfpfMjIG0p1CuqyuNdG8qqXXIHALeb9Kp 37bTyNF2w9r7x+jA+6XteB8/jRyXmDg99zcdKouZfjXx0Ui6e0/hw7UPEB58 8UQRD40U1LvGvL/2A4wyCbxP5qSRD7/XxmiqfwDpN5/sP2+hkfEnPdjSz/RB y5YDTqZLFOwy/seoOLwHJL5tEixaoODkwoR6rVsP+KT8JcAxT0GY4Sr/lFkP GJ5yZe38SYHCZb+yDIkeMMty2+MyQcGdjzyrubXvYZPS8JjpAAVKbSGy9Plu OKxwmc32LQWsb1usHR27IJV/rY/lDQWfeI4x3jbpAsaXJz5nNlDwv6mtD5NV umDiz3nvpXoKIsMjQ4w5u8AwPzqjsIqCJTLts2HuOzg8YrBcV0BBj+JlW4v5 TqgQHT21KYkC2cjuZAPxDmAbv55AS6QgPjhRTvpPO5zOPxyw9i8FHruPLWl1 t8O5Pcq7GeIpMF6907DLqx0ueOVMisdQ8NHa0861vw3UTd1YJsIomJfzUrP8 txUkuP6q2edHQYIknxGh2ww/1mjxHr4UiAS+prNJNoMd28lTXT7on8Pmm1ma 4eeL7RL37lOQE9+b7fK2CfaFZWjNe1EwHS14S1OzCY5dEs2TukNBrXiBvpPu W5AwvGgXe5uCvx56XWiVegvcTfu6WNH9Jkd3aW97C0nmpPucGwUxem7MZV1v 4IvCFrZ3LhRoZNuqXTB5A3Y1MQx0Bwp46iUtUh0aQbRwV/dF9B9ehW36Ro3A oLtHeOIWBTa7JUNEFRvhatBl4Q3o76uaZw4wNkKSR5gbaU+BcP6NH5PhDTB7 I/Acgy0FzWW9x/qqX0OB6s7r3jb4+toZYzXJV8Dcx3pPFr33kZR8CNcrsL5l WDFpTYG/f7/j8n/10HCvNcoYPaWWdm1XWz0MaxwqUbGiIGI69dg7+3qwMYjp OH6Jgntfi445VtXBkjWrDjta4ydLnk96HXzeLt/23gJ/n7fS2rmhdcDd0zlg ibaQ+3rtrHUdsI2aMYWaU/C+mmtgjKMOJP2Fv/JdxHl6ZsY8c7UWroVO/566 QEF95p/oxDO1kMaTu1KP/riFTeuGSi04sO4svYlO4rT00N9RC1v8hSboZhQw NZw3942sAYEr8nuL0QwvSzVc7GqAY+Gb6hO0bMznG9HHa8C1j4f9JFrNICTV 9r9q+C3i+7rbFO/P2LLniUvVMFK31FCMDkte0606Vg1GUTLRMWj7DWPRxvzV kJK8N8cSXefk3C7YXgU2ldMz2uh8B1F11edV4N32dOUQ+v1w7dkonyqIjK20 Y0CnjH91fKNYBc5Kqr2T5ynotLZlTebD1z9tYehF7xP7bZb5qxLGj/9Jz0Jb yAgaKGdVQtlo2rIFukOd0rojXAkjUr+YTqEjitgmXy9XgLqL4Q9A16tsFCDf V8BARLuWCFq+f5qp7VEFcOpylXKitRXJgwOWFaBBsa4womu5nrSKkBVwy+rL 3IQJ5sW7NBv5pXKoj41JG0QnMglNsneXQwu9WbwH/e40wyR3TjlUmA05tqDn vmVL6ASUQ7WtXmA9Wvyr55U8m3Jg1PK+Xo4Ot2u7rqlWDsXS01wFaO2ShQXW neXAZEt5ZaFth/TfbFgrAyEFifw0tDAvmSz2qQwO9H9MTUS7efDrupaWgUWE z7k49BM46rMcUQbf0yPbo9EhPktszx3KYOr0PVoUOsyxMNPvVBnEDRXOhKPz jjYJh/1TBnsfJ0Y9QTMthuxvYSuD8piS5TB0QZ91+KGpUrina8O1/nz/xrTt Dc2lkDkiMrzuqNTnnr7PS8Ey1dAmAk0NtfreelgK9M5b8eufJ/P16myATSko PJ/0i0GbtA/cf6dRCvn2/wjHo33b71Mqe0rB7kq2VRK6j6Voz5dNpfBvz4ez 6eibmW0VGaMlYL8ktLR+Py5/2HsvtqEE2DhnifX7NVC2U74itQTSLGsOrN/P RReutI1+JWAjs/K6Dl2vYOzval0CHvWctGa09T69DF7NEkjIdxnoQjP6uNYP iJdA3mKLWT86sEcysZO5BC7RlMhZtECkxsDBlmK4fLwzfhXNOyTQE59VDG3V mjHMOB9uuTV1R4KK4b7iOwtR9K1wvZefTxXD0dcmUgfRKz7pajOHi4HbqzyY WJ/nvBcM4rzFwBk5ymu6Pr+uAbs4PhVB1K198rZojpleodqqImB/IDPjgf5l lHEzKqEIYs4/2pqIPlFbqldhXQRcCbo3C9ClMVY3N2sXgaZIo2UjGnY6CrpL FUHap9Yf0+ioiVClrvlCkI3u8ln/fxlt2aZd8qEQjj+9m8Rnup7vTRz1lYVQ e6H2lio60alrRdO3EByPOKomorsGj0Rt4y+EXw+X9ErR8kLOGuNrBeBNL33b ge4Q47n8dbQAVq7SGWiYF12se89JFxaAndVRJyu0+1tWWzX9AjCvL+29iw78 2+Qgj0IB3Facjo9BK9+mJDeKFoDTU+GL79CWJp8Ipbl8iI92D1LF/DJa6Z3n CM+HGQcrdnO0ypfW2I47+cAQdWnGE+08omCRaZUPNW1aLRXoIH2O0rKj+ZAT HTQkj3mpzvk0T+pzHpwO9GzUwDzd6dIzaSCVB6PB5MgVtJ2f7oduvjy4caTX 8DHaaPBu1g2GPCi+s1+yB13lmuU535cLxNPTEZcxn+siuKeUfHJh8+jHnDjM c+0dHL4ar3LweYXYBnSks8HN+89yQPrX/Y5pdEToDcE5hxwwIvczgyXuZ4dz dZfEcmA6CnJG0K0L/2sI9c+GAeI9KOE+GbramjNi+hK2KmTRrqP//Bf/hE32 JVyO0WWORY+5bXxwnf0lHFXzHVtFbzZNtm2pyYIaPameOtxXVNrM7EaxLGAr EEw1ukLBb4PJS2LLLyCk38UuAF1kMGwV+P4FVJnyONagz1e/oonlvgClLTYS e69SsJ3Lj2HC5gW8dwg7tIpOuckClfTn0LzNaWf2dQpOVQ0OazVmgFWhNoyi +Rt7YrJSMkBVPjFQEPdpg0zPD6X7GTDtK1IQgE7ylnMaJTOAMSZC8PoNzNMo /0W96nS498ajVQb3cU8bS5huXRroS39KGsJ9/iB0UtDmWwr84tO7IuhIQbvS R/bg5hTwcS7RMULbq7EI9GengMrINYs2dI2Ua8mISwr0XD3RVO5EwfWWYKcX W1NAJuIMWwz2h+6tsV8+ySdDkBeTrQ32DRFRhqtPcxIhOf10Rwo69JjR881P E3GftcFXtO4nmVORXomg9zldyxT7S3cvw0FO/US4xsa2aOBBQayZgpfrYgJU EdvOqd7FfRT3ee+YWgK83JM+KY59yPmk6KTzTBxs4dohaYGGb2Y8Kk1xwNno aRuLVjt7/75iShzor4qucGCf4trZoFJ6Lg7a2f9IrqBDnBZ+dDXFguvCvopW 7GN7nusLnMt9BoNBFxbt/TFPq5IyDsRFQ7NHgGgmmuu5stYZj2gwEO7XHkVz 5w36pZpGA3/BoWDjAApOM1fzlQtFg3hm9JByIPYnFz+N4qSncF6nzIczCPuo vUlgZ14U9Do/9s4MpUD65w57pckIAJUnheNoGXEJjey2COjIqf4kjn3R75Xq hGZuBPy2G2ROQQe5X+yadYrAawn92RMKrm5+GLODMQLir8gfehSBednI0fZk dzi471Z9YhyN83wlvKPeOww8VvZsj0QHN9e5tV4Jg2sJ3MFdaJ1XMXlLJ8Pg 9rtYbR3sq+rtXrvzhcMgc033j+IzCh7ecw7Krw4F3qNBcjviMA/4uqSqGELh eXaiclMCBQvx/wxlqwaDtqxiLoUe7TAw0xcMhgrJATZZ7MvaSkEnxBeCoLt/ JCIJDXPxXpbpQcBtH9Xrjv1a4MHw2G72IKDPbGTbm4J9qjKgImAkEEyPFY07 plPwTeS+/40Cf0j4tcmk5yX2QyOPsJg2P5Ad7yW2ZlPw1rWDxTPbD+RWFliU 0SMKNCog2A/IxEWTLHQqYeu4R98P0q0nB+/lULApylv9BN0XuMenrffmYX8Q 2cRJ/PCBjZujpS8VUuCoTS/aLHcfrtrOVwaVU/Bl0fVcjLQXiL0XSahCf/gz tfuboBf0Sihfm0JvmnmzqrfZC1SZzcu0KiiQK9rlM1N6F26dP3KEsRL3vbSo shLHXThTMZN5E88bWYlSMtpNHjAgFPVMqZaCwYC/Ww9cug07LLJW/fG8wtDY 264g7gKTuSL789AKTRuSNVlcYO3ZYc0+tGjhkWeu086wTVOF3NVIgQvPYxmN QmeYXTQnytHM3fr1/qrOEMrbdmMEz0MnlPK0wi87Yc9PfyXRTIHr0JXxkBYH kN949rxbO75fATn7aMoeGrk+WMWhmQzOHn/aYw9vRn6erUO/mqqqb6i2x/7G usrcgfNdauzuEWoPZ2qaZaPQFsail0zk7EHkwRnfnE6c950fdxjz2UHI4KGa ji7MN35CfWvwdRimTwV19lKwkZZyyof/Mrj/imh0/Iz54KB2XCzAHGL9U98w DOP3Cd3v5F1oDPF3tLZtH8N9ZVpbIGykD4f1+ou5p3A+H2wX9nutDVuWPR/n /MD8Z1j8LMGkCvuGCzji5ijIVrEazzuiCCw/6858xfOlyrKgJ+f3w/BVf+Lj 1CL+XxxGRcVM9oOkBnPR3d8U6H+fJwSe74aL/6kKvV2mQPKLdFeSjhD0EsXn Z1ZwHrIDpUYTeSAr5KZF53+Yr/zKfEeit0F8cW5l9CoFu2PkBefdmODjz3O9 h/9g3ps3pgufo4HoFnpGLrqxUd1o++wSoVdg0yK8huc/ne1fprBLVW2orXBE c2dnLtaMjhHOG+YYa9Fyzu5ka/YQwcwhy7KKNhZ1FdPRoBNi8yHDEhQFLFd/ 5ha6dREJywGP9dEv/rYNk9VrJg5UDvvfRL8X/mfrI/FXhGH4cLA/+to+1dfZ nJWEuV5GYwL6g6qV1InNhYRT39OiPLSlXPw9afmXBL/t/PK6E1js+g5xvCS4 8rmJfLSFhy5c/Z5FCDCmNKzb/ki+om9kFpHcydBVgA5/1JJyfimT2P9kfLAI PfdYW8zo1Qtizvvfd2XoYGuR4y+8M4gjyRPs5ejYAxOaOhczCBZFmu66GUXH 2P4mMggX/4CGdc/c3jR8aiWdeFAiXlyBXo24bLfsmE4Iv45/XIX+dWD0zyaH NOIma/qbde+Y91ULN0gjHHLvbKhGM724IXlCJo0Iex3iuG5lemyn1mIqYb3f /GwNeusgu6zOnVTC3pwesm6dV6FKR81SCXlLkaZ1b7pt3fk/MpXgCBSQr0Uz nPGPXN6YSiSxddqve3ZWQC3oewqxwmOYse4SfR8n3eYUwqQ7fXDdUYWWY4df phBMji28deiPBmbn1EJSiP8DwxpmGQ== "]]}}}, Axes->True, AxesLabel->{ FormBox["\"N\"", TraditionalForm], FormBox["\"P\"", TraditionalForm]}, AxesOrigin->{0, 0}, Method->{}, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.662307784461307*^9, {3.662308988996522*^9, 3.6623090148145676`*^9}, 3.662346696966625*^9}] }, Open ]] }, WindowSize->{1546, 847}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (January 25, 2013)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[579, 22, 1824, 56, 130, "Input"], Cell[2406, 80, 392, 12, 31, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2835, 97, 1103, 33, 52, "Input"], Cell[3941, 132, 1640, 51, 98, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5618, 188, 184, 4, 31, "Input"], Cell[5805, 194, 334, 10, 31, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6176, 209, 189, 3, 31, "Input"], Cell[6368, 214, 187, 5, 31, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6592, 224, 292, 6, 31, "Input"], Cell[6887, 232, 378, 13, 46, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7302, 250, 184, 3, 31, "Input"], Cell[7489, 255, 229, 7, 78, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7755, 267, 1922, 54, 52, "Input"], Cell[9680, 323, 5344, 94, 216, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15061, 422, 1826, 53, 52, "Input"], Cell[16890, 477, 6267, 110, 447, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[23194, 592, 1793, 51, 52, "Input"], Cell[24990, 645, 6392, 112, 447, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[31419, 762, 167, 3, 31, "Input"], Cell[31589, 767, 17271, 293, 479, "Output"] }, Open ]] } ] *) (* End of internal cache information *)