# Update on bug in Maple 9.5 plot3d

Discussion in 'Maple' started by John Starrett, Nov 28, 2004.

1. ### John StarrettGuest

I am plotting a solution for a known chaotic system of three first order
ODEs, along with their isosurfaces, which are obtained by setting the
derivative equal to zero for each of the three equations. The change in
the solution in the x, y and z direction should be zero through the
surfaces Isurf1, Isurf2 and Isurf3 respectively. When plotted, this
displays (usually) incorrectly:

DE1:=diff(x(t),t)=-z(t);
DE2:=diff(y(t),t)=x(t)-y(t);
DE3:=diff(z(t),t)=alpha*x(t)+y(t)^2+beta*z(t);

DE1a:=subs(alpha=3.1,beta=0.5,DE1);
DE2a:=subs(alpha=3.1,beta=0.5,DE2);
DE3a:=subs(alpha=3.1,beta=0.5,DE3);

SPROTT:=DEplot3d({DE1a,DE2a,DE3a},{x(t),y(t),z(t)},
t=0..300,stepsize=.05,[[x(0)=.1,y(0)=.1,z(0)=.1]],linecolor=black,thickness=1):

Isurf1:=implicitplot3d({z=0}, x=-9..9, y=-9..9, z=-9..9,
axes=boxed,color=blue):
Isurf2:=implicitplot3d({x-y}, x=-9..9, y=-9..9,
z=-9..9,axes=boxed,color=yellow):
Isurf3:=implicitplot3d({z=-6.2*x-2*y^2}, x=-9..9, y=-9..9, z=-9..9,
axes=boxed,color=red):

display(Isurf1,Isurf2,Isurf3,SPROTT);

However, when the variables y and z are interchanged in the definitions
of the ODEs,

DE1:=diff(x(t),t)=-y(t);
DE2:=diff(z(t),t)=x(t)-z(t);
DE3:=diff(y(t),t)=alpha*x(t)+z(t)^2+beta*y(t);

the plot displays correctly (usually).

What is especially troubling is that sometimes it plots correctly and
sometimes it doesn't. I have done this literally dozens of times and can
find no pattern or clue as to when I will need to interchange the
variables y and z to get this to plot properly.

John Starrett, Nov 28, 2004