中文摘要：

证明了具有多频激励源混频构成的一阶微分电路也能诞生混沌.一阶非自治动态电路,当仅加入一个激励源时,受迫振荡呈现周期态;当加入多个不同频激励源时,诞生的受迫振荡呈现混沌态;以三个不同频的激励源为例,证明混沌振荡的诞生,仅不过是振荡周期的充分延长.可以用谐波平衡原理与功率平衡定理求微分方程的主谐波解.求解结果的正确性可用仿真相图验证.

英文摘要：

This paper proves that the first order differential circuit which is constituted by mixing of multi-excitation source with different frequency can also produce chaos. Regarding the first order non-autonomous circuits, the forced oscillation shows periodic status when only one ex- citation source is added. The forced oscillations display non-periodic status when multi-excitation source are added. Taking three excitation source as example, this paper proves that the births of chaotic oscillations are from sufficient extension of oscillation cycle. The main harmonic compo- nents in the differential equations can be solved by using the principle of the harmonics balance and power balance theorem. The correctness of solving results can be verified by phase portrait plotted by simulation.