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: ***