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 paper, following Kaldor's approach, is written with the intention of interpreting fluctuations of economic systems (i.e trade cycles). In particular, a new discretized Kaldor model is proposed, which is also useful to explain what appears to be random and unpredictable, such as economic...

Business cycles are oscillations in the economy because of recessions and expansions. In this paper we investigate the oscillation of the gross domestic product as a result of its relations with the other main macroeconomic variables such as capital, consumption, and investment.There is a...

This paper, written with the intention of formulating a macroeconomic model of trade cycles - following Kaldor's approach - explains the fluctuations of economic systems by using some numerical instruments. The reason for choosing a chaotic model will become clear as will the implications which...

Business cycles are oscillations in economy because of recessions and expansions. In this paper we investigate the oscillation of the Gross Domestic Product (GDP) as a result of its relations with the other main macroeconomic variables such as capital, consumption and investment. There is a...

In this Chapter, we provide the definitions, notions and examples relevant for the analysis of the dynamical systems of interest to us in the remainder of this book. We start with with a description of dynamical systems and we provide a taxonomy. Then, we define continuous-time dynamical systems...

In this chapter, the Logistic Map is taken as the example demonstrating the generic stability properties of fixed points and limit cycles, in dependence of the strength of nonlinearity. To identify attracting periodic orbits, we use the Schwarz derivative. The chapter ends with an application of...

Many dynamical systems depend on parameters. One may expect that small variations of the parameters produce no significant changes in the orbits. As was shown in Chap. 3 for the Logistic Map, even in simple cases, there exist critical values such that, moving the parameters through them, the...

In this chapter, we first precise the concept of dynamical systems, and then we introduce the concept of chaos, which is characterized by a sensitive dependence on initial conditions. To quantify this, dynamical (Lyapunov exponents) and probabilistic (dimensions) measures are introduced.