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Abstract: The extensiveness of producing chaos in the low order circuits can be realized by means of various mixing of multi-frequency components in the nonlinear device. This paper introduce that the forced oscillations may display chaotic status when two-excited sources are added to first order circuit. When one excited source is added tosecond order circuits , the self-excited and external excited frequency components are mixed in the nonlinear device. The mixing oscillations also may display chaotic status. For example Van der pol circuit, the self-excited frequency is independent to parameters of external excited source ;and depend on the circuit parameter LC. If circuit parameter maintain invariant, the self-excited frequency maintains fix, but the external excited frequencies are changed, thus commonly fundamental frequency is changed, the essentially variation of the patterns of mixing oscillations will happen. For conservative circuit, the self-excited frequencydepend on the voltage of external excitation, It has not fixed self-excited frequency. In whole process of mixing oscillations, the self-excited frequency vary with voltage of external excitation. Thus the lossless circuit constituted by the conservative circuit and excited source can display more sufficiently chaotic patterns. The non-periodic oscillation possess sufficiently or infinity long cycle, but it cannot display the close of trajectory in the simulation interval finally, therefore it is considered as non-periodic . It sometimesexhibits chaotic properties and shape ; sometimesexhibits non-chaotic character. Its main harmonic components also can be found by power balance theory and harmonic analysis method.
Key words: nonlinear oscillation; non- periodic oscillation; chaotic state; periodic state; coordinate system ; mixing
The Chaotic Oscillations of Low-Order Circuits.pdf
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