center manifold-08.nb

该程序用来处理微分方程系统的,用来化简一个微分系统的,特别是高维的系统,用来计算中心流行

    \(\(\((a - c)\)\^2\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \((a + \
c)\)\)\/\(c\ \((\(-a\^3\) - a\^2\ c + 5\ a\ c\^2 + c\^3)\)\)\)], "Output"],

Cell[BoxData[
    \(\(-\(\(\@\(a\ \((\(-a\) + c)\)\)\ \((a + c)\)\ \((a\^2 + 
                c\^2)\)\)\/\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \
\((a\^3 + a\^2\ c - 5\ a\ c\^2 - c\^3)\)\)\)\)\)], "Output"],

Cell[BoxData[
    \(\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \((3\ a\^2 + 2\ a\ c - c\
\^2)\)\)\/\(a\^3 + a\^2\ c - 5\ a\ c\^2 - c\^3\)\)], "Output"],

Cell[BoxData[
    \(\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \((a + c)\)\^3\ \((a\^4 \
- 4\ a\^2\ c\^2 - 2\ a\ c\^3 - c\^4)\)\)\/\(4\ a\ c\^2\ \((a\^6 + 2\ a\^5\ c \
- 6\ a\^4\ c\^2 - 9\ a\^3\ c\^3 + 8\ a\^2\ c\^4 + 7\ a\ c\^5 + c\^6)\)\)\)], \
"Output"],

Cell[BoxData[
    \(\(-\(\(\@\(a\ \((\(-a\) + c)\)\)\ \((a + c)\)\^2\ \((a\^3 + a\^2\ c - 
                a\ c\^2 + 
                c\^3)\)\)\/\(2\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \
\((a\^3 + a\^2\ c - 5\ a\ c\^2 - c\^3)\)\ \((a\^3 + a\^2\ c - 2\ a\ c\^2 - 
                c\^3)\)\)\)\)\)], "Output"],

Cell[BoxData[
    \(\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \((a + c)\)\^4\ \((a\^3 \
+ a\^2\ c - a\ c\^2 + c\^3)\)\)\/\(4\ a\ c\^2\ \((a\^6 + 2\ a\^5\ c - 6\ a\^4\
\ c\^2 - 9\ a\^3\ c\^3 + 8\ a\^2\ c\^4 + 7\ a\ c\^5 + c\^6)\)\)\)], "Output"],

Cell[BoxData[
    \(\(3\ \((\(-a\) + c)\)\ \((a + c)\)\^3\ \((\(-a\^3\) - 5\ a\^2\ c - 3\ a\
\ c\^2 + c\^3)\)\ \((a\^3 + a\^2\ c - a\ c\^2 + c\^3)\)\ \[Pi]\)\/\(16\ c\^2\ \
\((\(-a\^3\) - a\^2\ c + 5\ a\ c\^2 + c\^3)\)\ \((a\^6 + 2\ a\^5\ c - 6\ a\^4\
\ c\^2 - 9\ a\^3\ c\^3 + 8\ a\^2\ c\^4 + 7\ a\ c\^5 + c\^6)\)\) + \(3\ \
\((\(-a\) + c)\)\ \@\(a\ \((\(-a\) + c)\)\)\ \((a + c)\)\^2\ \((a\^4 - 4\ \
a\^2\ c\^2 - 2\ a\ c\^3 - c\^4)\)\ \((a\^5 + 3\ a\^4\ c - 6\ a\^3\ c\^2 + 8\ \
a\^2\ c\^3 - 3\ a\ c\^4 + c\^5)\)\ \[Pi]\)\/\(16\ a\ c\^2\ \((a\^5 + a\^4\ c \
- 6\ a\^3\ c\^2 - 2\ a\^2\ c\^3 + 5\ a\ c\^4 + c\^5)\)\ \((a\^6 + 2\ a\^5\ c \
- 6\ a\^4\ c\^2 - 9\ a\^3\ c\^3 + 8\ a\^2\ c\^4 + 7\ a\ c\^5 + c\^6)\)\) - \(\
\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \((\(-a\^3\) - 5\ a\^2\ c - 3\ a\
\ c\^2 + c\^3)\)\ \((\(\@\(a\ \((\(-a\) + c)\)\)\ \@\(\(a\ c\ \((\(-a\) + \
c)\)\)\/\(a + c\)\)\ \((a\^4 + 4\ a\^3\ c - 2\ a\^2\ c\^2 - 6\ a\ c\^3 - \
c\^4)\)\)\/\(a\ c\ \((a\^4 - 6\ a\^2\ c\^2 + 4\ a\ c\^3 + c\^4)\)\) + \
\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \((a\^4 + 4\ a\^3\ c - 2\ a\^2\
\ c\^2 + 2\ a\ c\^3 - c\^4)\)\)\/\(c\ \((a\^4 - 6\ a\^2\ c\^2 + 4\ a\ c\^3 + \
c\^4)\)\))\)\ \[Pi]\)\/\(12\ c\ \((\(-a\^3\) - a\^2\ c + 5\ a\ c\^2 + c\^3)\)\
\) - \(5\ \@\(a\ \((\(-a\) + c)\)\)\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\)\ \((a\^4 + 4\ a\^3\ c - 2\ a\^2\ c\^2 + c\^4)\)\ \((\(\@\(a\ \((\(-a\) \
+ c)\)\)\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \((a\^4 + 4\ a\^3\ c - \
2\ a\^2\ c\^2 - 6\ a\ c\^3 - c\^4)\)\)\/\(a\ c\ \((a\^4 - 6\ a\^2\ c\^2 + 4\ \
a\ c\^3 + c\^4)\)\) + \(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \((a\^4 \
+ 4\ a\^3\ c - 2\ a\^2\ c\^2 + 2\ a\ c\^3 - c\^4)\)\)\/\(c\ \((a\^4 - 6\ a\^2\
\ c\^2 + 4\ a\ c\^3 + c\^4)\)\))\)\ \[Pi]\)\/\(12\ a\ c\ \((a\^4 - 6\ a\^2\ c\
\^2 + 4\ a\ c\^3 + c\^4)\)\) + 
      1\/24\ \((\(\@\(a\ \((\(-a\) + c)\)\)\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\
\(a + c\)\)\ \((a\^4 + 4\ a\^3\ c - 2\ a\^2\ c\^2 - 6\ a\ c\^3 - \
c\^4)\)\)\/\(a\ c\ \((a\^4 - 6\ a\^2\ c\^2 + 4\ a\ c\^3 + c\^4)\)\) + \
\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \((a\^4 + 4\ a\^3\ c - 2\ a\^2\
\ c\^2 + 2\ a\ c\^3 - c\^4)\)\)\/\(c\ \((a\^4 - 6\ a\^2\ c\^2 + 4\ a\ c\^3 + \
c\^4)\)\))\)\^2\ \[Pi] - 
      1\/4\ \((\(-\(\(\@\(a\ \((\(-a\) + c)\)\)\ \((a + c)\)\^2\ \((a\^3 + 
                        a\^2\ c - a\ c\^2 + c\^3)\)\ \((a\^4 + 4\ a\^3\ c - 
                        2\ a\^2\ c\^2 + 2\ a\ c\^3 - 
                        c\^4)\)\)\/\(2\ c\ \((a\^3 + a\^2\ c - 5\ a\ c\^2 - 
                        c\^3)\)\ \((a\^3 + a\^2\ c - 2\ a\ c\^2 - 
                        c\^3)\)\ \((a\^4 - 6\ a\^2\ c\^2 + 4\ a\ c\^3 + 
                        c\^4)\)\)\)\) - \(\((\(-a\) + c)\)\ \((a + c)\)\^2\ \
\((a\^3 + a\^2\ c - a\ c\^2 + c\^3)\)\ \((a\^5 + 3\ a\^4\ c - 6\ a\^3\ c\^2 - \
2\ a\^2\ c\^3 - 3\ a\ c\^4 - c\^5)\)\)\/\(2\ c\ \((a\^3 + a\^2\ c - 5\ a\ \
c\^2 - c\^3)\)\ \((a\^3 + a\^2\ c - 2\ a\ c\^2 - c\^3)\)\ \((a\^5 + a\^4\ c - \
6\ a\^3\ c\^2 - 2\ a\^2\ c\^3 + 5\ a\ c\^4 + c\^5)\)\) + \(\((\(-a\) + c)\)\ \
\((a + c)\)\^2\ \((\(-a\^3\) - 5\ a\^2\ c - 3\ a\ c\^2 + c\^3)\)\ \((a\^4 - 4\
\ a\^2\ c\^2 - 2\ a\ c\^3 - c\^4)\)\)\/\(4\ c\^2\ \((\(-a\^3\) - a\^2\ c + 5\ \
a\ c\^2 + c\^3)\)\ \((a\^6 + 2\ a\^5\ c - 6\ a\^4\ c\^2 - 9\ a\^3\ c\^3 + 8\ \
a\^2\ c\^4 + 7\ a\ c\^5 + c\^6)\)\) + \(\((\(-a\) + c)\)\ \@\(a\ \((\(-a\) + \
c)\)\)\ \((a + c)\)\^3\ \((a\^3 + a\^2\ c - a\ c\^2 + c\^3)\)\ \((a\^5 + 3\ a\
\^4\ c - 6\ a\^3\ c\^2 + 8\ a\^2\ c\^3 - 3\ a\ c\^4 + c\^5)\)\)\/\(4\ a\ c\^2\
\ \((a\^5 + a\^4\ c - 6\ a\^3\ c\^2 - 2\ a\^2\ c\^3 + 5\ a\ c\^4 + c\^5)\)\ \
\((a\^6 + 2\ a\^5\ c - 6\ a\^4\ c\^2 - 9\ a\^3\ c\^3 + 8\ a\^2\ c\^4 + 7\ a\ \
c\^5 + c\^6)\)\) + \(2\ \@\(a\ \((\(-a\) + c)\)\)\ \@\(\(a\ c\ \((\(-a\) + c)\
\)\)\/\(a + c\)\)\ \((a\^4 + 4\ a\^3\ c - 2\ a\^2\ c\^2 + c\^4)\)\ \((b + \
\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\ \((a\^4 + 4\ a\^3\ c - 2\ a\^2\
\ c\^2 + 2\ a\ c\^3 - c\^4)\)\)\/\(c\ \((a\^4 - 6\ a\^2\ c\^2 + 4\ a\ c\^3 + \
c\^4)\)\))\)\)\/\(a\ c\ \((a\^4 - 6\ a\^2\ c\^2 + 4\ a\ c\^3 + c\^4)\)\))\)\ \
\[Pi]\)], "Output"],

Cell[BoxData[
    \(\(-\(\((\((a\^13\ \((3 + 8\ c)\) + 
                6\ c\^12\ \@\(a\ \((\(-a\) + c)\)\)\ \((1 + 
                      2\ b\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\))\) + 
                a\^12\ \((63\ c\^2 + 3\ \@\(a\ \((\(-a\) + c)\)\) + 
                      c\ \((30 - 22\ \@\(a\ \((\(-a\) + c)\)\))\))\) - 
                a\ c\^11\ \((11\ c\^2 - 
                      96\ b\ \@\(a\ \((\(-a\) + c)\)\)\ \@\(\(a\ c\ \((\(-a\) \
+ c)\)\)\/\(a + c\)\) + c\ \((3 + 26\ \@\(a\ \((\(-a\) + c)\)\))\))\) + 
                a\^4\ c\^8\ \((291\ c\^2 + 
                      c\ \((60 + 74\ \@\(a\ \((\(-a\) + c)\)\))\) + 
                      3\ \@\(a\ \((\(-a\) + c)\)\)\ \((17 - 
                            48\ b\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\))\))\) + 2\ a\^8\ c\^4\ \((413\ c\^2 + 
                      c\ \((\(-81\) + 402\ \@\(a\ \((\(-a\) + c)\)\))\) + 
                      6\ \@\(a\ \((\(-a\) + c)\)\)\ \((1 - 
                            37\ b\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\))\))\) - 2\ a\^10\ c\^2\ \((185\ c\^2 + 
                      6\ c\ \((\(-5\) + 33\ \@\(a\ \((\(-a\) + c)\)\))\) + 
                      3\ \@\(a\ \((\(-a\) + c)\)\)\ \((11 - 
                            14\ b\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\))\))\) + a\^3\ c\^9\ \((\(-69\)\ c\^2 + 
                      7\ c\ \((9 + 22\ \@\(a\ \((\(-a\) + c)\)\))\) + 
                      12\ \@\(a\ \((\(-a\) + c)\)\)\ \((2 - 
                            13\ b\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\))\))\) + 3\ a\^11\ c\ \((21\ c\^2 + 
                      c\ \((31 - 66\ \@\(a\ \((\(-a\) + c)\)\))\) + 
                      2\ \@\(a\ \((\(-a\) + c)\)\)\ \((1 + 
                            2\ b\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\))\))\) + a\^9\ c\^3\ \((\(-315\)\ c\^2 + 
                      5\ c\ \((\(-27\) + 86\ \@\(a\ \((\(-a\) + c)\)\))\) + 
                      12\ \@\(a\ \((\(-a\) + c)\)\)\ \((\(-11\) + 
                            6\ b\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\))\))\) + 2\ a\^2\ c\^10\ \((\(-43\)\ c\^2 + 
                      c\ \((9 - 10\ \@\(a\ \((\(-a\) + c)\)\))\) + 
                      6\ \@\(a\ \((\(-a\) + c)\)\)\ \((2 + 
                            13\ b\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\))\))\) + a\^5\ c\^7\ \((22\ c\^2 + 
                      c\ \((\(-9\) + 28\ \@\(a\ \((\(-a\) + c)\)\))\) + 
                      12\ \@\(a\ \((\(-a\) + c)\)\)\ \((1 + 
                            66\ b\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\))\))\) + 2\ a\^6\ c\^6\ \((\(-350\)\ c\^2 + 
                      c\ \((\(-3\) + 52\ \@\(a\ \((\(-a\) + c)\)\))\) + 
                      3\ \@\(a\ \((\(-a\) + c)\)\)\ \((\(-21\) + 
                            88\ b\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\))\))\) - 2\ a\^7\ c\^5\ \((\(-131\)\ c\^2 + 
                      c\ \((6 + 274\ \@\(a\ \((\(-a\) + c)\)\))\) + 
                      3\ \@\(a\ \((\(-a\) + c)\)\)\ \((1 + 
                            104\ b\ \@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\
\))\))\))\)\ \[Pi])\)/\((24\ a\ c\^2\ \((a\^3 + a\^2\ c - 5\ a\ c\^2 - \
c\^3)\)\^2\ \((a\^5 + a\^4\ c - 3\ a\^3\ c\^2 - 2\ a\^2\ c\^3 + 2\ a\ c\^4 + 
                c\^5)\))\)\)\)\)], "Output"]
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