Abstract The extensiveness of producing chaos in the lower order differential circuit can be correctly cognized by means of  building proper coordinate system. If taking excited component as a coordinate measure, first order differential circuit also can build three-dimensional coordinate system. The graphical solutions of the differential equation can be described by an space curve. This paper proves that the forced oscillation of first order dynamic circuits of non-autonomous emerge periodic status when only a excited source is added. The forced oscillations display chaotic status when two-excited source are added. The births of chaotic oscillations are from sufficient extension of oscillation cycle. The second order nonlinear differential circuits are analyzed further in this paper. When external excited sources are added to Van der pol circuit, mixing oscillation may emerge chaotic status. If circuit parameter maintain invariant, only the common fundamental frequency of multi-harmonic excited source is changed, the essentially variation of the shape and properties of oscillations will happen. This is important contributions of analysis method of frequency domain. The shape and properties of phase portrait after mixing depend on the high-low of common fundamental frequency of taking part in mixing component.

Key words; nonlinear oscillation; chaos; coordinate system; space curve; phase portrait

The chaotic oscillations of low order .pdf