Lineaaristen 2x2-systeemien faasitasoluokittelua

Nielu

with(linalg):with(DEtools):with(plots):
A:=matrix(2,2,[-3,1,1,-3]);
eigenvects(A);
       [-4, 1, {[ -1, 1 ]}], [-2, 1, {[ 1, 1 ]}]

v1:=vector([1,1]);v2:=vector([-1,1]);
z[1]:=c[1]*exp(-2*t);z[2]:=c[2]*exp(-4*t);
y:=z[1]*v1+z[2]*v2;
evalm(y);
                 [ c[1] exp(- 2 t) + c[2] exp(- 4 t),

                 c[1] exp(- 2 t) - c[2] exp(- 4 t) ]

(rivimuoto)
v1:=convert(v1,matrix): v2:=convert(v2,matrix):
y:=z[1]*op(v1)+z[2]*op(v2);

                            [ 1 ]                   [  1 ]
       y := c[1] exp(- 2 t) [   ] + c[2] exp(- 4 t) [    ]
                            [ 1 ]                   [ -1 ]

(sarakemuoto)

(Versio V.3):
DEplot(A, [x,y], -10..10, {[0,0,2],[0,0,4],[0,-6,0],[0,-4,0],[0,0,-2],
  [0,0,-4],[0,6,0],[0,4,0]}, stepsize=.2, x=-10..10, y=-10..10,
  arrows=THIN,title=`Nielu`);










 Satula 
A:=matrix(2,2,[2,-4,1,-3]);
eigenvects(A);
   [-2, 1, {[ 1, 1 ]}], [1, 1, {[ 4, 1 ]}]


 Reaaliset, erimerkkiset


                            [ 1 ]               [  4 ]
       y := c[1] exp(- 2 t) [   ] + c[2] exp(t) [    ]
                            [ 1 ]               [  1 ]


DEplot(A, [x,y], -10..10, {[0,0,2],[0,0,4],[0,-6,0],[0,-4,0],[0,0,-2],
  [0,0,-4],[0,6,0],[0,4,0],[0,5,5],[0,-5,-5],[0,5,4],[0,5,3],[0,5,2],
  [0,-5,-2]}, stepsize=.1, x=-10..10, y=-10..10, arrows=THIN,title=`Satula`);



This page created by

<Heikki.Apiola@hut.fi>

Last update 14.10.96