restart; with(plots); with(DEtools); f := r*x-sin(x) EQ1 := f = 0; r x - sin(x) = 0 EQ2 := diff(f, x) = 0; r - cos(x) = 0 EQ2 := factor(EQ2); r - cos(x) = 0 BIFpt := solve({EQ1, EQ2}, {r, x}); {r = cos(RootOf(-tan(_Z) + _Z)), x = RootOf(-tan(_Z) + _Z)} BIFpt2 := [[-4/27, 1/3], [0, 1]]; > BIFdiag := implicitplot(f = 0, r = -.5 .. 1, x = -14 .. 14, style = POINT); > BIFptPLOT := plot(BIFpt2, style = POINT, color = BLUE, symbol = BOX); display(BIFdiag, BIFptPLOT);

Well it works now, I don't know why:

 

#BIFURCATION DIAGRAM PROCEDURE
restart:
with(plots):
#xexpr is the logistic function to be iterated (we always start off at x=1/2, which will eventually attract).
#[ra,rb] is the range of the parameter.
#acc is the number of points sampled in [ra,rb]
Bifurcation := proc(initialpoint,xexpr,ra,rb,acc)
   local p1,hr,A,L1,i,j,phi:
   global r,L2:
   hr := unapply(xexpr,x);
   A := Vector(600):
   L1 := Vector(acc*500):
   for j from 1 to acc+1 do
      r := (ra + (j-1)*(rb-ra)/acc):
      A[1] := hr(initialpoint):
      for i from 2 to 500 do
         A[i] := evalf(hr(A[i-1])):
      end do:
      for i from 1 to 400 do
         L1[i+400*(j-1)] := [r,A[i+100]]:
      end do:
   end do:
   L2 := {seq(L1[i], i = 1..acc*400)}:
   p1 := pointplot(L2):
   return(p1):
end proc:
**must unassign('r') before each use of the procedure
EXAMPLES:
unassign('r'):
P1 := Bifurcation(1/2,x*x*x+r*x,3,4,250):
unassign('r'):
P2 := Bifurcation(1/2,x*x*x+r*x,3.5,3.6,10):
P1; P2;

But nothing shows up. Do you know what's wrong?

Hey Robert,

 

when I try and evaluate the function x^3+r*x I get an error regarding the kernel, do you know what's wrong?

Forget alll the previous posts,

 

which old command corresponds to which new command?

AppendColumns, AppendRows, and BlockMatrix are available in the Mathematica kernel functions Join and ArrayFlatten.

Mathematica says:

AppendColumns, AppendRows, and BlockMatrix are available in the Mathematica kernel functions Join and ArrayFlatten.
TakeRows, TakeColumns, TakeMatrix, and SubMatrix are available in the Mathematica kernel function Take.

The later has four commands which use one now. How do I know if it's performing the same operation?

c = 0;
For[z = 0, z < 5, z++
  For[n = 0, n < 5, n++,
   c = c + 4/((2 n + 1) \[Pi]) Sin[(2 n + 1) (2 \[Pi])/T t - k z];
        ]
  Print[c]
   ]

 

How do I plot the sum of these fourier coefficients?

 

Numerical, have any ideas for Mathematica?

Okay here is the Maple equivalent of this general solution I obtained from Mathematica:

 

0 < Tau and 0 < HBar and Pi(HBar)*(1+2*_C1)/t(Tau) = x and (0 <= _C1 and 1+2*_C1 < 4*_C2 and 1/2*Pi*sqrt(HBar^2*(-(1+2*_C1)^2+16*_C2^2)/Tau^2) = t or 0 < 1+2*_C1 and 2*_C1 < 1+4*_C2 and 0 <= _C2 and Pi*sqrt(-HBar^2*(-1+2*_C1-4*_C2)*(3+2*_C1+4*_C2)/Tau^2) = 2*t) and `in`(_C1,_C2)

 

 

Now If I want to output all values of x, would a nested if/else in a do loop give me all values of x and t?

I did this with each condition seperately however I'm suspicious.

Would you mind downloading a .pdf file then?

My computer is too slow to load the mathematica file. Is there a way I can upload it here or would that not even matter?

 

I've been stuck on this stupid thing for 3 weeks and I need to get this thing done but I don't know the source of the problem and the Mathematica forums is too "unhelpful" in dealing with this issue.

I notice that Maple is alot slower than Mathematica, is there anyway I can optimize its speed?

How can I declare tau to be real with the above commands? Why is it so much more elegant with mathematica?

Nevermind

How would you get an expression in terms of tau explicitly with Maple?

 

no tau = 1 etc.

How would oyu go about doing that?