Business cycle theory concerns the description and explanation of the observed ups and downs of main macroeconomic variables. After the early attempts to provide informal and non mathematical explanations, based on verbal arguments and empirical observations, the business cycle theory has been mainly considered a problem of mathematical economics after the works by Samuelson [28] and Hicks [16]. So, a business cycle model is now considered a dynamic model, usually formulated in the framework of the theory of dynamical systems, whose mathematical structure allows for fluctuations in major macroeconomic variables. A broad, and purely formal, classification of business cycle models distinguishes between linear and nonlinear, continuous and discrete time models.