MaplePrimes - answers and comments on Question, Another Dynamical System

evalf

Preben Alsholm — Sat, 01 Dec 2012 22:12:24 Z

Using evalf helps:

LinearAlgebra:-Eigenvalues(J(25/8, 5/18, -5/8));
evalf(%);
You will see that 2 of the eigenvalues are imaginary and have positive real parts. The third is (real and) negative.

For a bunch of orbits you could try something like this:

interface(warnlevel=0); #Initially you may not want to turn warnings off as they do give you some valuable information.
bg:=pointplot3d(pts,symbol=solidsphere,symbolsize=20,color=blue):
x0:=-2: y0:=-1: z0:=-2: dx:=6: dy:=3: dz:=3: N:=4:
t1:=-10: t2:=5:
DEplot3d({sys},[x(t),y(t),z(t)],t=t1..t2,[seq(seq(seq([x(0)=x0+i*dx/N,y(0)=y0+j*dy/N,z(0)=z0+k*dz/N],k=1..N-1),j=1..N-1),i=1..N-1)],linecolor=red,x=x0..x0+dx,y=y0..y0+dy,z=z0..z0+dz,thickness=2,stepsize=.01):
display(%,bg);

Admittedly a rather confusing picture.

Thank you

escorpsy — Mon, 03 Dec 2012 10:59:10 Z

dear Markiyan Hirnyk , what can i do to be a solid person ? do you mean 'escorpsy' ?

however in https://controls.engin.umich.edu/wiki/index.php/Recorded_Lectures , you download lecture 16 .

thank you Preben Alsholm , new.mw , buw how the last command to show critical points didnt work .

The output without bg

Markiyan Hirnyk — Sat, 01 Dec 2012 23:05:16 Z

mess?

PatrickT — Mon, 03 Dec 2012 14:35:51 Z

@Markiyan Hirnyk Is that a limit cycle (similar to Lorenz) in the middle there or just a mess?

No answer

Markiyan Hirnyk — Mon, 03 Dec 2012 18:23:30 Z

@PatrickT I don't know it.

A line left out

Preben Alsholm — Mon, 03 Dec 2012 18:45:27 Z

It appears that I left out a line defining 'pts':

solve({f(x, y, z) = 0, g(x, y, z) = 0, h(x, y, z) = 0}, {x, y, z});
pts:=map(subs,[%],[x,y,z]);

Another thing: In your worksheet you use 2D input and apparently somehow a space was interpreted as a multiplication sign in the definition of bg:

bg:=pointplot3d([[-1, 2/5, 0], [25/8, 5/18, -5/8]], symbol = solidsphere, symbolsize = 20, color = blue):

Advice: Don't use 2D input. I never do.