ParametricPlot[Evaluate[Join[{x[t],y[t]}/.NDSolve[{x'[t]==y[t],y'[t]==-.2y[t]-.26Sin[x[t]],x[0]==0,y[0]==#},{x[t],y[t]},{t,-30,30}][[1]]&/@{-2.5,-2.2,-2,-1.7,Sequence@@Range[-1.5,-1,.2],-1.02,Sequence@@Range[0,1.5,.2],1.02,1.7,2,2.2,2.5},{x[t],y[t]}/.NDSolve[{x'[t]==y[t],y'[t]==-.2y[t]-.26Sin[x[t]],x[0]==-2Pi,y[0]==#},{x[t],y[t]},{t,-30,30}][[1]]&/@Range[0,1,.2],{x[t],y[t]}/.NDSolve[{x'[t]==y[t],y'[t]==-.2y[t]-.26Sin[x[t]],x[0]==2Pi,y[0]==#},{x[t],y[t]},{t,-30,30}][[1]]&/@Range[0,1,.2]]],{t,-20,20},PlotRange->{{-6,6},{-3,3}},PlotStyle->Red,DisplayFunction->Identity,AxesLabel->TraditionalForm/@{angle,angular velocity},Background->White,LabelStyle->Directive[12]]