1cm.mac is from the book "Perturbation Methods, Bifurcation Theory and
2Computer Algebra" by Rand & Armbruster (Springer 1987)
3
4It performs center manifold reduction for ordinary differential
5equations.
6
7The first example is from p31.  maxima-5.9.0 cvs reproduces the
8results from the book.
9
10(C1) load("./cm.mac");
11(D1)                               ./cm.mac
12(C2) cm();
13ENTER NO. OF EQS.
143;
15ENTER DIMENSION OF CENTER MANIFOLD
162;
17THE D.E.'S MUST BE ARRANGED SO THAT THE FIRST 2 EQS.
18REPRESENT THE CENTER MANIFOLD.  I.E. ALL ASSOCIATED
19EIGENVALUES ARE ZERO OR HAVE ZERO REAL PARTS.
20ENTER SYMBOL FOR VARIABLE NO. 1
21x;
22ENTER SYMBOL FOR VARIABLE NO. 2
23y;
24ENTER SYMBOL FOR VARIABLE NO. 3
25z;
26ENTER ORDER OF TRUNCATION
272;
28ENTER RHS OF EQ. 1
29D x /DT =
30y;
31ENTER RHS OF EQ. 2
32D y /DT =
33-x-x*z;
34ENTER RHS OF EQ. 3
35D z /DT =
36-z+alpha*x^2;
37dx
38-- = y
39dT
40dy
41-- = - x z - x
42dT
43dz          2
44-- = ALPHA x  - z
45dT
46CENTER MANIFOLD:
47              2                          2
48     2 ALPHA y    2 ALPHA x y   3 ALPHA x
49[z = ---------- - ----------- + ----------]
50         5             5            5
51FLOW ON THE C.M.:
52                            2                          2
53 dx      dy        2 ALPHA y    2 ALPHA x y   3 ALPHA x
54[-- = y, -- = - x (---------- - ----------- + ----------) - x]
55 dT      dT            5             5            5
56
57
58
59The second example is from page 35, and again the results in the book
60are reproduced by maxima-5.9.0-cvs.
61
62(C3) cm();
63ENTER NO. OF EQS.
644;
65ENTER DIMENSION OF CENTER MANIFOLD
663;
67THE D.E.'S MUST BE ARRANGED SO THAT THE FIRST 3 EQS.
68REPRESENT THE CENTER MANIFOLD.  I.E. ALL ASSOCIATED
69EIGENVALUES ARE ZERO OR HAVE ZERO REAL PARTS.
70ENTER SYMBOL FOR VARIABLE NO. 1
71mu;
72ENTER SYMBOL FOR VARIABLE NO. 2
73x;
74ENTER SYMBOL FOR VARIABLE NO. 3
75y;
76ENTER SYMBOL FOR VARIABLE NO. 4
77z;
78ENTER ORDER OF TRUNCATION
793;
80ENTER RHS OF EQ. 1
81D MU /DT =
820;
83ENTER RHS OF EQ. 2
84D x /DT =
85mu*x+y;
86ENTER RHS OF EQ. 3
87D y /DT =
88mu*y-x-x*z;
89ENTER RHS OF EQ. 4
90D z /DT =
91-z+alpha*x^2;
92dMU
93--- = 0
94dT
95dx
96-- = y + MU x
97dT
98dy
99-- = - x z + MU y - x
100dT
101dz          2
102-- = ALPHA x  - z
103dT
104CENTER MANIFOLD:
105                    2            2
106       28 ALPHA MU y    2 ALPHA y    8 ALPHA MU x y   2 ALPHA x y
107[z = - -------------- + ---------- + -------------- - -----------
108             25             5              25              5
109
110                                                               2            2
111                                                  22 ALPHA MU x    3 ALPHA x
112                                                - -------------- + ----------]
113                                                        25             5
114FLOW ON THE C.M.:
115                                                  2            2
116 dMU      dx             dy          28 ALPHA MU y    2 ALPHA y
117[--- = 0, -- = y + MU x, -- = - x (- -------------- + ----------
118 dT       dT             dT                25             5
119
120                                                   2            2
121       8 ALPHA MU x y   2 ALPHA x y   22 ALPHA MU x    3 ALPHA x
122     + -------------- - ----------- - -------------- + ----------) + MU y - x]
123             25              5              25             5
124
125
126Local Variables: ***
127mode: Text ***
128End: ***