> restart; with(DEtools,DEplot): with(plots,display): with(linalg,matrix,eigenvects):

En övergång från egentlig nod till spiral sker för följande matris när K=-3.

> matrix([[1,-2],[2,K]]);

> ekv1:=D(x)(t)=x(t)-2*y(t):

> tmax:=[1,5,5,2,4,4,4,5,5]:

> init1a:=seq([x(0)=0.5*k,y(0)=1],k=-1..2):
init1b:=seq([x(0)=0.5*k,y(0)=-1],k=-2..1):
init1:=init1a,init1b:

> i:=1: k:=0.25*(i-13):
ekv2:=D(y)(t)=2*x(t)+(k-1)*y(t):
fig||i:=DEplot([ekv1,ekv2],[x,y],t=0..tmax[i],[init1],x=-1..1, y=-1..1):

> init2a:=[x(0)=-1,y(0)=-1],[x(0)=-0.5,y(0)=1],[x(0)=0,y(0)=1], [x(0)=1,y(0)=1],[x(0)=1,y(0)=0.5],[x(0)=0.5,y(0)=-1],[x(0)=0,y(0)=-1]:
init2b:=seq([x(0)=(-1)^j,y(0)=(-1)^j/1.828],j=1..2),
seq([x(0)=(-1)^j*0.5471, y(0)=(-1)^j],j=1..2):
init3b:=seq([x(0)=(-1)^j,y(0)=(-1)^j/1.640],j=1..2),
seq([x(0)=(-1)^j*0.6096, y(0)=(-1)^j],j=1..2):
init4b:=seq([x(0)=(-1)^j,y(0)=(-1)^j/1.422],j=1..2),
seq([x(0)=(-1)^j*0.7035, y(0)=(-1)^j],j=1..2):

> for i from 2 to 4 do
k:=0.25*(i-13): ekv2:=D(y)(t)=2*x(t)+(k-1)*y(t):
fig||i||1:=DEplot([ekv1,ekv2],[x,y],t=0..tmax[i],[init2a],x=-1..1, y=-1..1):
fig||i||2:=DEplot([ekv1,ekv2],[x,y],t=0..5*tmax[i],[init||i||b],x=-1..1, y=-1..1,stepsize=0.1):
od:

> init5a:=init2a,[x(0)=0.5,y(0)=1],[x(0)=-0.5,y(0)=-1]:

> for i from 5 to 9 do
k:=0.25*(i-13): ekv2:=D(y)(t)=2*x(t)+(k-1)*y(t):
fig||i:=DEplot([ekv1,ekv2],[x,y],t=0..tmax[i],[init5a],x=-1..1, y=-1..1, stepsize=0.1):
od:

> L:=[fig1, display({fig21,fig22}), display({fig31,fig32}), display({fig41,fig42}), seq(fig||k,k=5..9)]:

> display(L,insequence=true);

>