Exogenous Versus Endogenous for Chaotic Business Cycles

Abstract

We propose a novel approach to generate chaotic business cycles in a deterministic setting. Rather than producing chaos endogenously, we consider aggregate economic models with limit cycles and equilibriums, subject them to chaotic exogenous shocks and obtain chaotic cyclical motions. Thus, we emphasize that chaotic cycles, which are inevitable in economics, are not only interior properties of economic models, but also can be considered as a result of interaction of several economical systems. This provides a comprehension of chaos (unpredictability, lack of forecasting) and control of chaos as a global economic phenomenon from the deterministic point of view.We suppose that the results of our paper are contribution to the mixed exogenous-endogenous theories of business cycles in classification by P.A. Samuelson [76]. Moreover, they demonstrate that the irregularity of the extended chaos can be structured, and this distinguishes them from the generalized synchronization. The advantage of the knowledge of the structure is that by applying instruments, which already have been developed for deterministic chaos one can control the chaos, emphasizing a parameter or a type of motion. For the globalization of cyclic chaos phenomenon we utilize new mechanisms such that entrainment by chaos, attraction of chaotic cycles by equilibriums and bifurcation of chaotic cycles developed in our earlier papers.

Homoclinic and Heteroclinic Motions in Economic Models with Exogenous Shocks

“…Chaos in the sense of Devaney [2] as well as the one obtained through period-doubling cascade [13] were investigated in our study [14] for economic models perturbed with exogenous shocks. It was shown in the paper [15] that exogenous shocks can cause economic models to exhibit chaotic business cycles. Other chaos generation techniques in systems of differential equations can be found in [16][17][18][19][20][21][22][23][24][25][26].…”

Persistence of Li–Yorke chaos in systems with relay

“…Our suggestion may be a key to explain why the weather unpredictability is observed everywhere. This is true also for unpredictability and lack of forecasting in economics [21,22]. To complete the explanation of weather and economical unpredictability as global phenomena by the analysis of interconnected models, we need to argument persistence of chaos of a model against chaotic perturbations as solutions of another similar models.…”