Is it possible to use a Volterra series to generate subharmonics?
Check out this paper.  I would have made a comment but not high enough rep.  

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&amp;arnumber=1211087&amp;url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F81%2F27258%2F01211087

Looks like you need multiple in to get subharmonics in Volterra series

The abstract states "Subharmonic generation is a complex nonlinear phenomenon which can arise from nonlinear oscillations, bifurcation and chaos. It is well known that single-input-single-output Volterra series cannot currently be applied to model systems which exhibit subharmonics. A new modeling alternative is introduced in this paper which overcomes these restrictions by using local multiple input single output Volterra models. The generalized frequency-response functions can then be applied to interpret systems with subharmonics in the frequency domain."