Plot Poincare map in order to analyze chaos?

Questions
,
1

Consider the following code:

U[t] + 3 U[t]^2 + 6 V[t] + 3 V[t]^2 + 5 W[t] + 2 W[t]^2 + 4 U[t]*V[t] == 2 U'[t] ;
            6 U[t] + 3 U[t]^2 + 3 V[t] + 4 V[t]^2 + 8 W[t] + 4 W[t]^2 + 3 U[t]*V[t] == V'[t];
            5 U[t] + 3 U[t]^2 + 5 V[t] + 3 V[t]^2 + 8 W[t] + 4 W[t]^2 + 8 U[t]*V[t]+ Q*Sin[100*t] == W'[t] + 2 W''[t];
            U[0] == V[0] == W[0], U'[0] == V'[0] == W'[0]==0.0001
    Q=const

I need to plot a Poincare map with W [t], W '[t]. I am having trouble. I thank everyone.

2

I will show a numerical solution

q = {U[t] + 3 U[t]^2 + 6 V[t] + 3 V[t]^2 + 5 W[t] + 2 W[t]^2 + 
     4 U[t]*V[t] == 2 U'[t], 
   6 U[t] + 3 U[t]^2 + 3 V[t] + 4 V[t]^2 + 8 W[t] + 4 W[t]^2 + 
     3 U[t]*V[t] == V'[t], 
   5 U[t] + 3 U[t]^2 + 5 V[t] + 3 V[t]^2 + 8 W[t] + 4 W[t]^2 + 
     8 U[t] V[t] + Q*Sin[100*t] == W'[t] + 2 W''[t]};
ic = {U[0] == a, V[0] == a, W[0] == a, W'[0] == 10^-4};
Q = -1; a = -1/10; tm = 1;
p = NDSolveValue[{eq, ic}, {W[t], W'[t]}, {t, 0, tm}];
{ParametricPlot[p, {t, 0, tm}, PlotRange -> All, 
  AxesLabel -> {"W", "W'"}], 
 Plot[p, {t, 0, tm}, PlotRange -> All, AxesLabel -> {"t", ""}]}

pm.png
pm.png1131×542 53.5 KB