The dynamics of a parametric frequency divider is treated rigorously. The complicated process of subharmonic generation is shown to be related to the Mathieu equation. Due to its similarity to the well known RL diode circuit, the system is capable of generating chaos as well as subharmonics. Hence, the circuit can not merely be regarded as a core for constructing frequency synthesizers but it can probably serve as a noise generator as well. Furthermore, recently suggested methods of chaos control may enable the output to be switched rapidly between different types of subharmonics modes of operation.
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