r=0.2;
tend=100;
eqn1=x1'[t]-r*x1[t]+x2[t]+x1[t]^3+x1[t]*x2[t]^2==0;
eqn2=x2'[t]-x1[t]-r*x2[t]+x2[t]^3+x2[t]*x1[t]^2==0;
eqn3=x1[0]==1.0;
eqn4=x2[0]==0;

sol=NDSolve[{eqn1,eqn2,eqn3,eqn4},{x1,x2},{t,0,tend}];

ParametricPlot[Evaluate[{x1[t],x2[t]}/.sol],{t,0,tend},PlotRange->All, Background->White,AxesLabel->{x1,x2},LabelStyle->Directive[16]]