Schumpeterian Business Cycles The basic idea of Schumpeterian Business Cycles is that new technologies require creative destruction but will yield positive growth. These two opposing forces have impacts onto the real economy at different times, which will create fluctuations around the trend. 

Romer (1986) has these effects in an explicit growth model, but he neglects the business cycle fluctuations.

Has there been any literature of business cycles based on the idea of Schumpeterian Growth?
I will toot my own horn and cite - Phillips and Wrase. (2006) "Is Schumpeterian ‘Creative Destruction’ a Plausible Source of Endogenous Real Business Cycle Shocks?," Journal of Economic Dynamics and Control, vol. 30 no. 11 pp. 1885-1913.

We found it difficult to match the volatility using Schumpterian mechanisms alone.  The business cycle asymmetries from our model were also exactly backward.  That is, a sudden discovery leads to a jump in output which slowly peters out.  While recessions tend to suddenly jump downward and then slowly recover.

The mechanism in our model was that an increase in productivity due to the discovery, leads to a reallocation of resources away from innovation toward production of output and this slows down the innovation process.