Polarplot warning for a semistable limit cycle...

Hey, i'm trying do demonstrate that a nonlinear system has a semistable limit cycle but i get a warning at the plot command saying "Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct" and i dont understand it. So i wonder if someone here could help me?

restart; with(PDEtools); with(plots);
eq1 := diff(x(t), t) = x(t)*(x(t)^2+y(t)^2-1)^2-y(t);
2
d              /    2       2    \
--- x(t) = x(t) \x(t)  + y(t)  - 1/  - y(t)
dt
eq2 := diff(y(t), t) = y(t)*(x(t)^2+y(t)^2-1)^2+x(t);
2
d              /    2       2    \
--- y(t) = y(t) \x(t)  + y(t)  - 1/  + x(t)
dt
tr := {x(t) = r(t)*cos(theta(t)), y(t) = r(t)*sin(theta(t))};
{x(t) = r(t) cos(theta(t)), y(t) = r(t) sin(theta(t))}
eq1b := dchange(tr, x(t)*eq1+y(t)*eq2, [r(t), theta(t)], simplify);
/ d      \       2 /        4         2\
r(t) |--- r(t)| = r(t)  \1 + r(t)  - 2 r(t) /
\ dt     /
eq1b := expand(eq1b/r(t));
d                    5         3
--- r(t) = r(t) + r(t)  - 2 r(t)
dt
eq2b := dchange(tr, y(t)*eq1-x(t)*eq2, [r(t), theta(t)], simplify);
2 / d          \        2
-r(t)  |--- theta(t)| = -r(t)
\ dt         /
eq2b := simplify(eq2b/(-r(t)^2));
d
--- theta(t) = 1
dt
sol1 := dsolve({eq1b, r(0) = r[0]}, r(t));
/      /  /     2  \
|      |  | r[0]   |          2     2
r(t) = exp|RootOf|ln|--------| (exp(_Z))  r[0]
\      \  \r[0] - 1/

2     2
- ln(r[0] + 1) (exp(_Z))  r[0]

/             2\
|(exp(_Z) - 1) |          2     2            2        2
- ln|--------------| (exp(_Z))  r[0]  + (exp(_Z))  _Z r[0]
\ exp(_Z) - 2  /

/     2  \
2     2         | r[0]   |             2
+ 2 (exp(_Z))  r[0]  t - 2 ln|--------| exp(_Z) r[0]
\r[0] - 1/

2
+ 2 ln(r[0] + 1) exp(_Z) r[0]

/             2\
|(exp(_Z) - 1) |             2                    2
+ 2 ln|--------------| exp(_Z) r[0]  - 2 exp(_Z) _Z r[0]
\ exp(_Z) - 2  /

/     2  \
2       | r[0]   |          2
- 4 exp(_Z) r[0]  t - ln|--------| (exp(_Z))
\r[0] - 1/

/             2\
2     |(exp(_Z) - 1) |          2
+ ln(r[0] + 1) (exp(_Z))  + ln|--------------| (exp(_Z))
\ exp(_Z) - 2  /

/     2  \
2                   2       | r[0]   |
- (exp(_Z))  _Z - 2 t (exp(_Z))  + 2 ln|--------| exp(_Z)
\r[0] - 1/

/             2\
|(exp(_Z) - 1) |
- 2 ln(r[0] + 1) exp(_Z) - 2 ln|--------------| exp(_Z)
\ exp(_Z) - 2  /

2                                    2
- (exp(_Z))  + 2 _Z exp(_Z) + 4 t exp(_Z) + r[0]  + 2 exp(_Z)

\\
||
- 1|| - 1
//
sol1 := simplify(sol1);
/      /   /     2  \
|      |   | r[0]   |               2
r(t) = exp|RootOf|-ln|--------| exp(2 _Z) r[0]
\      \   \r[0] - 1/

2
+ ln(r[0] + 1) exp(2 _Z) r[0]

/             2\
|(exp(_Z) - 1) |               2                    2
+ ln|--------------| exp(2 _Z) r[0]  - exp(2 _Z) _Z r[0]
\ exp(_Z) - 2  /

/     2  \
2         | r[0]   |             2
- 2 exp(2 _Z) r[0]  t + 2 ln|--------| exp(_Z) r[0]
\r[0] - 1/

2
- 2 ln(r[0] + 1) exp(_Z) r[0]

/             2\
|(exp(_Z) - 1) |             2                    2
- 2 ln|--------------| exp(_Z) r[0]  + 2 exp(_Z) _Z r[0]
\ exp(_Z) - 2  /

/     2  \
2       | r[0]   |
+ 4 exp(_Z) r[0]  t + ln|--------| exp(2 _Z)
\r[0] - 1/

/             2\
|(exp(_Z) - 1) |
- ln(r[0] + 1) exp(2 _Z) - ln|--------------| exp(2 _Z)
\ exp(_Z) - 2  /

/     2  \
| r[0]   |
+ exp(2 _Z) _Z + 2 t exp(2 _Z) - 2 ln|--------| exp(_Z)
\r[0] - 1/

/             2\
|(exp(_Z) - 1) |
+ 2 ln(r[0] + 1) exp(_Z) + 2 ln|--------------| exp(_Z)
\ exp(_Z) - 2  /

2
+ exp(2 _Z) - 2 _Z exp(_Z) - 4 t exp(_Z) - r[0]  - 2 exp(_Z)

\\
||
+ 1|| - 1
//
sol2 := dsolve({eq2b, theta(0) = theta[0]}, theta(t));
theta(t) = t + theta[0]
theta[0] := (1/4)*Pi;
1
- Pi
4
plot1 := polarplot([subs(r[0] = .1, rhs(sol1)), rhs(sol2), t = 0 .. 10], color = red);
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct
plot2 := polarplot([subs(r[0] = 2, rhs(sol1)), rhs(sol2), t = 0 .. 10], color = blue);
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct
display({plot1, plot2}, scaling = constrained, tickmarks = [4, 3], view = [-2 .. 2, -2 .. 2]);

How to put 1 to 12 around a circle like on clock f...

How to put number 1,2,3...12  around a circle, like a clock face using Maple code ?

Right now I can only do this manually by plotting a circle, then save the file and use Windos paint to

mannual put in the numbers

Transforming a polar plot from 2D into 3D...

I am using MAPLE 2016.1.

I have created an animation of points on a polarplot (2D), but would like it to be projected into 3D, with time t being the 3rd axis.  Here is my code for the polarplot animation:

with(plots);
Repltlist := proc (t) options operator, arrow; [[sin(t), 0], [cos(t), (1/3)*Pi], [cos(2*t), (2/3)*Pi]] end proc;
Impltlist := proc (t) options operator, arrow; [[-sin(3*t), 0], [-2*cos(t), (1/3)*Pi], [-cos(4*t), (2/3)*Pi]] end proc;
titleName := "Polar representation of time-dependence of degrees of freedom in configuration space"; captionName := "Re - red, Im - blue";
P := animate(polarplot, [Repltlist(t), color = "Red"], t = -Pi .. Pi, symbol = solidcircle, style = point, color = red, symbolsize = 12, frames = 100, gridlines = true);
Q := animate(polarplot, [Impltlist(t), color = "Blue"], t = -Pi .. Pi, symbol = solidcircle, style = point, color = blue, symbolsize = 12, frames = 100, gridlines = true);
R := display([P, Q], title = titleName, caption = captionName); R;

I have been trying use the plots[transform] to 'lift' this polarplot into 3D:

with(plottools); with(plots);

plrPt(2); f := proc (tt) options operator, arrow; plottools:-transform(proc (r, theta) options operator, arrow; [r, theta, tt] end proc) end proc; display((f(2))(plrPt(2)));

but the last command gives no output.

Can anyone help?

MRB
PS:  I am now attemptiing to do the lift to 3D by using a cylinderplot but would like know why the transform function is not able able to lift the polarplot into 3D.

Polarplot3d of ODE system solution...

I am trying to have the output of DETOOLS as 3dpolarplot. As in the following example:

EF := {2*(diff(w[2](t), t)) = 10, diff(w[1](t), t) = sqrt(2/w[1](t)), diff(w[3](t), t) = 0}; with(DEtools); DEplot3d(EF, {w[1](t), w[2](t), w[3](t)}, t = 0 .. 100, [[w[1](0) = 1, w[2](0) = 0, w[3](0) = 0]], scene = [w[1](t), w[2](t), w[3](t)], stepsize = .1, orientation = [139, -106])

how can I get the output as a polarplot in 3d where, w[2] and w[3] have range 0..2*pi.