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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Exogenous Versus Endogenous for Chaotic Business Cycles

Discontinuity, Nonlinearity, and Complexity 5(2) (2016) 101--119 | DOI:10.5890/DNC.2016.06.001

Marat Akhmet$^{1}$, Zhanar Akhmetova$^{2}$, Mehmet Onur Fen$^{1}$

$^{1}$ Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey

$^{2}$ Department of Economics, Australian School of Business, University of New South Wales, Sydney, NSW 2052, Australia

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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 [1]. 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 as entrainment by chaos, attraction of chaotic cycles by equilibriums and bifurcation of chaotic cycles developed in our earlier papers.


Z. Akhmetova is supported by a grant from the School of Economics, ASB, UNSW, Sydney, Australia. M.O. Fen is supported by the 2219 scholarship programme of TÜBITAK, the Scientific and Technological Research Council of Turkey.


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