How to Export this animation as a gif file for powerpoint presentation

Animate[
  Manipulate[
   ParametricPlot[ Evaluate[{x[t], v[t]} /.
    Quiet @ NDSolve[
     {x'[t] == v[t],
     v'[t] == μ (1 - x[t]^2) v[t] - x[t] + A*Cos[ω*t],
     x[0] == xv0[[1]], v[0] == xv0[[2]]}, {x[t], v[t]}, {t, 0, tt}]],
    {t, 0, tt}, ImageSize -> {450, 450}, PlotRange -> 4, 
    AxesLabel -> {TraditionalForm[x[t]], TraditionalForm[v[t]]},
    PlotStyle -> PointSize[.5]

  ],
  {{μ, 0.75, "parameter μ"}, 0, 3, 0.01, Appearance -> "Labeled"},
  {{ω, 0.75, "parameter ω"}, 0, 3, 0.01, Appearance -> "Labeled"},
  {{A, 0.75, "parameter A"}, 0, 3, 0.01, Appearance -> "Labeled"},
  {{xv0, {1, 1}}, {-4, -4}, {4, 4}, Locator}], {tt, 0, 200}, 
  AnimationRate -> 3, AnimationRepetitions -> 3, AnimationRunning -> True
]

Answer

You have to set values which are dynamic in Manipulate.

μ = .75; ω = .75; A = .075; xv0 = {1, 1};

Table pictures for different tt:

sol = Quiet@NDSolve[{x'[t] == v[t], v'[t] == μ (1 - x[t]^2) v[t] - x[t] + A*Cos[ω*t], 
                     x[0] == xv0[[1]], v[0] == xv0[[2]]
                    }, {x[t], v[t]}, {t, 0, 20}];

dat = Table[
            ParametricPlot[Evaluate[{x[t], v[t]} /. sol, {t, 0, tt}, 
                           PlotRange -> 4, AxesLabel -> {x[t], v[t]}]
            , {tt, .1, 20, .2}];

Create gif.

SetDirectory@NotebookDirectory[]
Export["gif.gif", dat]