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...

In this chapter, in Sect. 12.1 we provide a sketch of the Keynesian multiplier and the multiplier–accelerator model by Hansen and Samuelson. The description of the Kaldor model (Sect. 12.2) is introduced by the related literature (Sect. 12.2.1). As Kaldor described his model only...

Complex systems are characterized by deterministic laws (which often may be hidden) and randomness. A tool to analyse those systems is recurrence quantification analysis (RQA). RQA does not rely on any sort of assumption of stationarity and is not sensitive to singularities and transitions. It...

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...

When a system becomes unstable or noise becomes excessive, often regulations of the form of limiters (barriers obstructing excursion into undesired areas of the phase space) are imposed. It is hoped that by the influence of this element, the system can be calmed and its behaviour can be...

R.G. Goodwin mentioned that "economists will be led, as natural scientists have been led, to seek in nonlinearities an explanation of the maintenance of oscillation" (Goodwin, Econometrica 19(1), 1951); following this reasoning, we studied business cycles as if they were generated by nonlinear...

This chapter is dedicated to describe RQA applications in detecting spatio-temporal recurrent patterns of dynamical regimes of economic time series. Here we investigate the nature of economic dynamics and specifically of business cycles Orlando and Zimatore (Chaos, Solitons Fractals 110:82–94,...

Monetary responses to financial stress have recently become an important issue in macroeconomic and policy discussions in the USA as well as in the EU. In this paper, the authors study two regimes of monetary responses. While the fundamentals of an economy are assumed to have a long-run...