hopf.html

> with(DEtools):

> sys:={diff(x(t),t)=mu*x(t)+y(t)-x(t)*y(t)^2,diff(y(t),t)=-x(t)+mu*y(t)-y(t)^3};

$sys := {diff(y(t),t) = -x(t)-y(t)^3, diff(x(t),t) =...$

> mu:=-0.1:

> DEplot(sys,[x(t),y(t)],0..10,[[x(0)=0.1,y(0)=0],[x(0)=0.3,y(0)=0]],linecolour=[red,blue],stepsize=0.1);

> mu:=0:

> DEplot(sys,[x(t),y(t)],0..10,[[x(0)=0.15,y(0)=0],[x(0)=0.2,y(0)=0]],linecolour=[red,blue],stepsize=0.1);

> mu:=0.1:

> DEplot(sys,[x(t),y(t)],0..100,[[x(0)=0.1,y(0)=0],[x(0)=0.2,y(0)=0]],linecolour=[red,blue],stepsize=0.1);