In[24]:=
<<Local`NullclinePlot` f[x_, y_] := -Cos[y] + 2 y * Cos[y^2] * Cos[2 x]; g[x_, y_] := -Sin[x] + 2 Sin[y^2] * Sin[2 x]; NullclinePlot[{f[x, y], g[x, y]}, {x, -3.45, 4}, {y, -1.8, 4.2}, ShowEquilibria -> True, NullclineContourPlotPoints -> 120, NullclineShading -> True, AspectRatio -> 1.6]
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2. Coloring the Compass Directions