Exogenous Versus Endogenous for Chaotic Business Cycles Marat Akhmet a, $^{∗}$, Zhanar Akhmetova $^{b}$, Mehmet Onur Fenc $^{a}$Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey $^{b}$Department of Economics, Australian School of Business, University of New South Wales, Sydney, NSW 2052, Australia $^{c}$Neuroscience Institute, Georgia State University, Atlanta, Georgia 30303, USA 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 equilib- riums, 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 mod- els, 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 the- ories 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. Keywords: Business cycle models; Exogenous shocks; Period-doubling cascade; Attraction of chaotic cycles; Chaotic business cycle Business cycles are a commonly accepted phenomenon in economics. However, we do not actually observe perfectly periodic motions in economic variables. Instead, economic data is highly irregular. One way to reflect this in economic models is to allow for stochastic processes. Deterministic differential equations can also be turned into a better picture of economic reality by introducing chaos. 1 arXiv:1509.01034v1 [nlin.CD] 3 Sep 2015 ∗ Corresponding Author Tel.: +90 312 210 5355, Fax: +90 312 210 2972, E-mail: marat@metu.edu.tr $^{1}$There exists a third approach, which is somewhere in-between the two, where iterated function systems generated by the optimal policy functions for a class of stochastic growth models converge to invariant distributions with support over fractal sets [62]. 1 1 Introduction Abstract