Manipulate[
Module[{f1,f2,x1,x2,sol,x,t,ode},
f1=x2;
f2=(-x1^2-x1-a)*x2-x1;
ode=x''[t]+(x[t]^2+x[t]+a)*x'[t]+x[t]==0;
sol=NDSolve[{ode,x[0]==1,x'[0]==0},x,{t,0,30}];
Grid[{
{Row[{"a = ",NumberForm[a,{4,2}]}]},
{
StreamPlot[{f1,f2},{x1,-5,5},{x2,-7,7},
ImageSize->300,
StreamPoints->{{{{1,0},Red},Automatic}}],
Plot[Evaluate[x[t]/.sol],{t,0,30},
PlotRange->{Automatic,{-4,4}},
ImageSize->300,
GridLines->Automatic,GridLinesStyle->LightGray,
PlotStyle->Red,
AxesLabel->{"time","x(t)"},
BaseStyle->12,
PlotLabel->"Solution to  x''+f[x] x' + x = 0"
]
}
}
]
],
{{a,-2,"a"},-2,1,0.1,Appearance->"Labeled"},
TrackedSymbols:>{a}
]