Exogenous Versus Endogenous for Chaotic Business Cycles

TL;DR

This paper introduces a new perspective on chaotic business cycles by demonstrating how external shocks to deterministic economic models can generate chaos, offering insights into predictability and control of economic fluctuations.

Contribution

It presents a novel approach to generate chaos through exogenous shocks in deterministic models, bridging exogenous and endogenous theories of business cycles.

Findings

Chaotic business cycles can be induced by external shocks in deterministic models.

Structured chaos allows for potential control using existing chaos control methods.

Mechanisms like entrainment and bifurcation influence chaotic cycle behavior.

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.