u-plane of one flavor theory

You can change the bare mass of the squark by moving the slider below,
in the normalization where the dynamical scale Λ of the gauge theory is one.
Three singular points in the u-plane are depicted by red/green/blue circles.

When | m | is sufficiently big,  you find one point in the outer region, and two points around the origin.
In the semiclassical language, the outer point is where the squark becomes massless, 
and the inner two points are where the monopole or dyon becomes massless. 

But there is no absolute distinction among the three, as you can see by changing m yourself.
For your reference, the point where the squark becomes massless classically is 
depicted by an purple open circle. 
Indeed, by changing the bare mass, you can make any of the red/green/blue points to be closest
to the classical squark point. This means you can continuously change a squark point 
to a monopole point, and vice versa.

You can animate it by clicking the "+" button in the top right corner, 
and choosing "Animate Bookmarks."

Manipulate[Show[Plot3Complex[(  u/.NSolve[(disc/.{m->pt[[1]] + pt[[2]] I})==0,u])],MLabel[pt],If[semi,Classical[pt],Graphics[]]],{{pt,{0,0},"m"},{-8,-8},{8,8}},{{semi,True,"classical squark point"},{True,False}},Initialization:>( disc=Discriminant[x^2(x-u)+m x  - 1,x];prev={0,0,0};
Distance[x_]:=Plus@@ ((#*#)& /@( Abs /@(x-prev)));
Reorder[list_]:=(xxx=SortBy[Permutations[list],Distance];prev=xxx[[1]]);
Plot3Complex[list_]:=Plot3Points[({Re[#],Im[#]})&/@ Reorder[list]];
Plot3Points[list_]:=Graphics[{{PointSize[Large],Red,Point[{list[[1]]}]},{PointSize[Large],Blue,Point[{list[[2]]}]},{PointSize[Large],Green,Point[{list[[3]]}]}},Axes->True,AspectRatio->1,PlotRange->{{-15,15},{-15,15}}];
MLabel[pt_]:=Graphics[{Style[Inset[m==Chop[pt[[1]]+I pt[[2]]],{Left,Top},{Left,Top}],FontSize->15]}];
RectanglePoint[pt_]:={Thick,Purple,Circle[pt,.5]};
Classical[pt_]:=Module[{m=(pt[[1]]+I pt[[2]])/2},Graphics[RectanglePoint[{Re[m^2],Im[m^2]}]]]),Bookmarks:>{"untitled":>{pt={0.`,6.700000000000001`},semi=True},"untitled 2":>{pt={0.20000000000000107`,0.`},semi=True},"untitled 3":>{pt={0.20000000000000107`,-7.1`},semi=True},"untitled 4":>{pt={-4.8`,-5.9`},semi=True},"untitled 5":>{pt={-5.4`,5.`},semi=True},"untitled 6":>{pt={0.`,6.700000000000001`},semi=True}}]

If you're curious, here is the Mathematica program for it :

Manipulate[Show[Plot3Complex[(  u/.NSolve[(disc/.{m->pt[[1]] + pt[[2]] I})==0,u])],MLabel[pt],If[semi,Classical[pt],Graphics[]]],{{pt,{0,0},"m"},{-10,-10},{10,10}},{{semi,True,"classical squark point"},{True,False}},Initialization:>( disc=Discriminant[x^2(x-u)+m x  - 1,x];prev={0,0,0};
Distance[x_]:=Plus@@ ((#*#)& /@( Abs /@(x-prev)));
Reorder[list_]:=(xxx=SortBy[Permutations[list],Distance];prev=xxx[[1]]);
Plot3Complex[list_]:=Plot3Points[({Re[#],Im[#]})&/@ Reorder[list]];
Plot3Points[list_]:=Graphics[{{PointSize[Large],Red,Point[{list[[1]]}]},{PointSize[Large],Blue,Point[{list[[2]]}]},{PointSize[Large],Green,Point[{list[[3]]}]}},Axes->True,AspectRatio->1,PlotRange->{{-20,20},{-20,20}}];
MLabel[pt_]:=Graphics[{Style[Inset[m==pt[[1]]+I pt[[2]],{Left,Top},{Left,Top}],FontSize->15]}];
RectanglePoint[pt_]:={Thick,Purple,Circle[pt,.5]};
Classical[pt_]:=Module[{m=(pt[[1]]+I pt[[2]])/2},Graphics[RectanglePoint[{Re[m^2],Im[m^2]}]]])]