V[x_,y_]:=x^4/4-x^2/2+y^2*x^2;
a=-1.5;
b=1.5;
plot1=ContourPlot[V[x,y],{x,a,b},{y,a,b},PlotPoints->100,Contours->30,FrameLabel->{"x","y"},LabelStyle->Directive[Bold, Black,Large]];
plot2=StreamPlot[{-x^3+x-2*y^2*x,-2*x^2*y},{x,a,b},{y,a,b},StreamColorFunction->Black];
Show[plot1,plot2]