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A troublesome case: the Dirac delta function

The shading algorithm is by no means infallible. For example, it needs a
discrete set of equilibrium points in order to proceed, while some functions
have an overabundance of critical points. The following example is based on a
step function and every point on or outside the unit disk is an equilibrium
point! To deal with these cases we have included a switch that calls upon the
alternative method alluded to earlier: a density plot of the sum of signs.
Setting the NullclineShadingMethod to SumOfSigns forces the alternative method
to be used. The results for this troublesome example are not ideal, but they are
roughly accurate, with a white region showing the region of equilibrium points
outside the unit disk.
*In[]:=*

Up to 3. More Examples