Quadratic non-linear oscillators

The solution behaviors of the differential equations of three quadratic non-linear oscillators (QNO) were studied. The qualitative theory of differential equations was used to draw some general conclusions. The results show that the quadratic oscillator equations have certain regions in the (x,y) phase space for which periodic solutions exist. The results also show that there exist other regions, that enclose the regions where periodic solutions occur, for which only unbounded motions take place.