@torabi Well, you didn't really answer my question about the amplitude: What does that mean when the attractor is rather complicated and not just a point?

So what I decided to do was to sample the y-values for various time values equidistantly spaced after an initial settling period.

The code follows.

## This assumes that you have executed the definition of my version of fdsolve given earlier.
## option remember in the procedure means that if you repeat any of this for the same
## A-value then it won't take long.
##That is why I stick to a previously defined list of A-values.
##
F:=omega*x-y^2;
G:=mu*(z-y);
H:=A*y-B*z+x*y;
params:={omega=-2.667,mu=10,B=1}; # A unassigned
## Order alpha, final time T, number of points N. All will be fixed in advance.
alpha:=0.89: T:=20: N:=2000:
solfu:=proc(AA,inits::[numeric,numeric,numeric]) option remember,system; local FGH;
if not AA::numeric then return 'procname(_passed)' end if;
FGH:=unapply~(eval([F,G,H],params union {A=AA}),t,x,y,z);
fdsolve(FGH,alpha,0..T,inits,N)
end proc:
## We shall be using two initial conditions inits1 and inits2:
inits1:=[.1,.1,.1]; inits2:=[-.1,-.1,-.1];
## The A values considered are:
Alist:=[seq(0..30,1)];
sol:=solfu(Alist[1],inits1); #Test (not wasted because of option remember)
plot(sol[..,[1,3]],labels=[t,y],size=[1200,default]);
## The following animation is not wasted because of option remember.
plots:-animate(plots:-spacecurve,[solfu(A,inits1)[..,2..4] ],A=Alist);
## For each A we pick points beginning with Nb and continuing with a spacing of n points.
## Thus we pick the points numbered Nb+i*n, i=0..floor((N-Nb)/n).
Nb:=N-1000; n:=50;
numpts:=floor((N-Nb)/n)+1; # Number of points chosen for each A
## The distance in time between points will be
n*T/N;
## The procedure Q produces a sequence of points for A given.
Q:=proc(A,inits::[numeric,numeric,numeric]) local sol;
sol:=solfu(A,inits);
seq([A,sol[Nb+i*n,3]],i=0..numpts-1)
end proc;
##
PtList1:=[seq(Q(A,inits1),A=Alist)]: # This is fast because of the animation done earlier.
plot(PtList1,style=point); p1:=%:
PtList2:=[seq(Q(A,inits2),A=Alist)]: # This takes a while.
plot(PtList2,style=point,color=blue); p2:=%:
plots:-display(p1,p2,labels=[A,y],size=[800,700],caption=typeset('alpha'=alpha));

The plot:

Because of option remember the following won't take long:

## It shows animations in A of the orbits from inits1 and inits2 in the same coordinate system.
use plots in
a1:=animate(spacecurve,[solfu(A,inits1)[..,2..4] ],A=Alist);
a2:=animate(spacecurve,[solfu(A,inits2)[..,2..4] ],A=Alist);
display(a1,a2)
end use;