# Plot Poincare map in order to analyze chaos?

Posted 5 months ago
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 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.
 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", ""}]}