poincare[d_,γ_,ω_,ndrop_,nplot_,psize_]:=(T=2 π/ω;
g[{xold_,vold_}]:={x[T],v[T]}/. NDSolve[{v'[t] == x[t]-x[t]^3-γ v[t]+d Cos[ω t],x'[t] == v[t],x[0] == xold,v[0]== vold},{x,v},{t,0,T}][[1]];
lp=ListPlot[Drop[NestList[g,{0,0},nplot+ndrop],ndrop],PlotStyle ->{PointSize[psize],Hue[0]},PlotRange ->All,AxesLabel ->{"x","v"}])

poincare[0.35,0.1,1.4,200,15000,0.002];

Show[lp,Epilog ->{GrayLevel[0.6],Thickness[0.006],Line[{{0.8,0.35},{0.8,0.67},{1.05,0.67},{1.05,0.35},{0.8,0.35}}]}]

poincare2[d_,γ_,ω_,ndrop_,nplot_,psize_,xmin_,xmax_,vmin_,vmax_]:=(T=2 π/ω;g[{xold_,vold_}]:={x[T],v[T]}/. NDSolve[{v'[t]==x[t]-x[t]^3-γ v[t]+d Cos[ω t],x'[t]==v[t],x[0]==xold,v[0]==vold},{x,v},{t,0,T}][[1]];
lp2=ListPlot[Drop[NestList[g,{0,0},nplot+ndrop],ndrop],PlotRange ->{{xmin,xmax},{vmin,vmax}},PlotStyle ->{PointSize[psize],Hue[0]},PlotRange->All,AxesLabel->{"x","v"},AxesOrigin ->{xmin,vmin},AspectRatio ->1])

poincare2[0.35,0.1,1.4,2000,100000,0.003,0.8,1.05,0.35,0.67];

Show[lp2,Epilog ->{GrayLevel[0.6],Thickness[0.006],Line[{{0.86,0.48},{0.91,0.48},{0.91,0.58},{0.86,0.58},{0.86,0.48}}]}]