In this chapter, we outline the reasons why economics has been concerned with non-linear dynamics, with a particular focus on business cycles and on economic growth. Using varying perspectives, we discuss the salient historical mathematical approaches to the problem and the results that were...

In this chapter, we describe growth and cycles in economics as a struggle between capitalists and workers. We first present the Phillips curve (which statistically relates unemployment with the rate of change of nominal wages) and then the Goodwin model. The latter reinterprets, in economical...

We present an extension of the Goodwin growth-cycle model that considers the rate of capacity utilization as a new variable in an adapted Lotka-Volterra system of differential equations. We derive a differential equation for the capacity utilization that is proportional to the difference between...