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• The discrete-time mathematical model of the macroeconomic system is presented. • The system is studied through topological classification, bifurcation analysis, Lyapunov exponents, and manifold theory. • A fuzzy based-activation feedback controller is proposed for the synchronization of the system. Economic systems, due to their substantial effects on any society, are interesting research subject for a large family of researchers. Despite all attempts to study economic and financial systems, studies on discrete-time macroeconomic systems are rare. Hence, in the current study, we aim to investigate dynamical behavior and synchronization of these systems. At first, the discrete-time mathematical model of the macroeconomic system is presented. Then, the system is studied through topological classification, bifurcation analysis, Lyapunov exponents, and manifold theory, which are powerful tools in the investigation of nonlinear systems. This way, the features of the system are disclosed, and the existence of chaos in the system is shown. For the adequate performance of the economy, the economic systems are desired to operate in a unified manner. To this end, in the present research, a fuzzy based-activation feedback controller is proposed for the synchronization of the system. To enhance the celerity and accuracy of the proposed control for synchronization purposes, it is equipped with a fuzzy logic engine. Finally, the numerical simulations of the synchronization are presented and compared with those of a conventional activation feedback control. Numerical results verify that the proposed control technique can successfully push the states of the response system to the desired value. [ABSTRACT FROM AUTHOR]

• We introduce for the first time in the literature a fractional-calculus-based artificial macroeconomic model. • A new system of fractional difference-order equations is proposed for the Goodwin model. • Using bifurcation diagrams, phase portraits and Lyapunov exponents among other measures, the characteristics of the new system are depicted. • We implement extensive simulations via a new hardware laboratory realization set up. In this novel research, through dynamical analysis, we introduce for the first time a fractional-calculus based artificial macroeconomic model, actually implemented in the Laboratory via a new hardware set up. Firstly, we propose a new model of a discrete-time macroeconomic system where fractional derivatives are incorporated into the system of equations. Using well-known tools and methods, including bifurcation diagrams and Lyapunov exponents, the characteristics of the system are disclosed, and the importance of the fractional-order derivative in the modeling of the system is shown. After that, a laboratory hardware realization is also carried out for the proposed system that provides further insight and a better understanding of the properties of the system. For the hardware realization an Arduino Due™ is chosen in which possess two analog output pins. Experimental results conspicuously illustrate the chaotic behavior of the system. Through the results of the hardware realization, phase portraits and bifurcation diagram of the system are demonstrated, and the effects of the parameters and fractional derivatives are studied. We believe the presented study and its results pave the way for future studies on the incorporation of fractional calculus into macroeconomic models. [ABSTRACT FROM AUTHOR]