So I'm not sure , but you know that at (u4,0), F = 5, and G=1, to the right and upwards respectively. On top of that the direction of the field arrows on each side on the nullclines change each time they pass a fixed point. So starting from (u4,0), with field arrow pointing up and right, you know that the field arrows above the fixed point, at u3, on the w nullcline will point left, and the arrows on the u nullcline on the left of u3 will point down, essentially opposite from the point (u4,0). I guess that you can do that across the plane for each fixed point and this way you find the direction of the field arrows, just by knowing the flow direction at (u4,0).
Hope that helps
