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Abstract Using nonlinear differential equations describe dynamic process of non-autonomous circuits of first-order. The functional relation among three dynamic variation can be displayed by a 3-demension space curve. In order to plot phase portrait of non-autonomous equation, this paper present a fresh 3-demension coordinate system. Its advantage is that the space curve is bounded when.
When the non-autonomous circuit of first ordercontains multi-excited sources with different frequencies, the output response of steady state of the multi-harmonics mixing in nonlinear device is a forced oscillation. Its shape and property depend on the composition of excited source. Itpossess universal regularity that the oscillation patterns vary with excited cycle. The variable law is identical for different energy store elements. The long-short of forced oscillation cycle depend on the low-high of common fundamental frequencies of excited sources. The oscillation cycle gradually extend, the patterns of phase portrait can progressively evolve to chaotic state from periodic state. The periodic state can obviously obtain a closed period orbit in the simulation interval, the closed orbit may be single circle or multi-circle. The phase portrait of chaotic state is much more complex than the periodic state, it cannot display the close of trajectory in the simulation interval finally, therefore it is considered as non-periodic chaos . The common characteristics of variable law of oscillation patterns are displayed by means of using two sorts of example with different energy store elements in this paper.
In fact, the numerical operation of modern simulation all are that using approximately rational number replace irrational number. Thus the phase portraits plotted by numerical simulation all are periodic, when the simulation time is sufficiently extended. It follows that the distinguish between periodic and chaotic state merely is long-short of oscillation cycle.
Key words:mixing; phase portrait; periodic state; chaotic state; commonly fundamental frequency
Two Sorts of Oscillation Patterns Arisen by Mixing.pdf
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