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This work investigates the economic growth problem of establishing a relation between the elasticity of substitution between production factors, capital and output per-capita levels when dealing with a non constant elasticity of substitution production function. Starting from a discrete-time setup, some definitions of elasticity of substitution associated to an attractor are proposed and a general method to measure it is suggested. Thanks to this methodology a government may select a proper economic policy in order to reduce production costs without decreasing the capitalisation trend of the economy. The method proposed is applied to the Solow’s type growth model with differential savings using a Variable Elasticity of Substitution (VES) production function with constant returns to scale. It is found that when shareholders save more than workers or the elasticity of substitution is higher than one, a country characterised by production functions with higher elasticity of substitution experiences higher capital and output per-capita equilibrium levels. On the other hand, when the elasticity of substitution is lower than one and workers save more than shareholders, an ambiguous relation between elasticity of substitution and asymptotic dynamics is shown.

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, 2018). Thus, after having devised a suitable model for business cycles such as that discussed in Chap. 16 and in References (Orlando, Math Comput Simul 125:83–98, 2016; 2018, https://doi.org/10.1007/978-3-319-71243-7_6), we look for an indicator that could show structural changes in a time series and that might be chaotic (Orlando and Zimatore, Indian Academy of Sciences Conference Series—Proceedings of the Conference on Perspectives in Nonlinear Dynamics—2016, vol. 1, pp. 35–41, Springer, Berlin, 2017, https://doi.org/10.29195/iascs.01.01.0009). More specifically we apply RQA and statistical techniques to real time series to: (1) find common properties if and where they do exist, (2) discover some hidden features of economic dynamics and (3) highlight potential indicators of structural changes in the signal (i.e. precursors of a crash).

Intermittent behavior of economic dynamics is investigated by a two-country model of Keynes–Goodwin type business cycles. Numerical simulations show that after an economic system evolves from weak chaos to strong chaos the system keeps its memory before the transition and its time series alternates episodically between periods of weakly and strongly chaotic fluctuations. In addition, we examine the intermittent phenomena from the view point of business cycle patterns near the crisis point.

In this paper, we present a complete mathematical characterization of a coefficient criterion for four-dimensional Hopf bifurcations. Then, we apply our criterion to two typical models of economic dynamics. We consider the two-region business cycle model by Puu [Nonlinear economic dynamics, Springer-Verlag, Berlin, 1997] and the dynamic optimization model by Dockner and Feichtinger [J. Econom. 53 (1991) 31]. These applications reveal that our criterion is operative and useful in analyzing the qualitative properties of general four-dimensional dynamic economic models with continuous time.