Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 529164, 23 pages
Research Article

Numerical Exploration of Kaldorian Macrodynamics: Enhanced Stability and Predominance of Period Doubling and Chaos with Flexible Exchange Rates

Toichiro Asada,1 Christos Douskos,2 and Panagiotis Markellos2

1Faculty of Economics, Chuo University, 742-1 Higashinakano, Hachioji, Tokyo 192-0393, Japan
2Faculty of Engineering, University of Patras, 26500 Patras, Greece

Received 16 May 2007; Accepted 17 March 2008

Academic Editor: Masahiro Yabuta

Copyright © 2008 Toichiro Asada et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We explore a discrete Kaldorian macrodynamic model of an open economy with flexible exchange rates, focusing on the effects of variation of the model parameters, the speed of adjustment of the goods market α, and the degree of capital mobility β. We determine by a numerical grid search method the stability region in parameter space and find that flexible rates cause enhanced stability of equilibrium with respect to variations of the parameters. We identify the Hopf-Neimark bifurcation curve and the flip bifurcation curve, and find that the period doubling cascades which leads to chaos is the dominant behavior of the system outside the stability region, persisting to large values of β. Cyclical behavior of noticeable presence is detected for some extreme values of a state parameter. Bifurcation and Lyapunov exponent diagrams are computed illustrating the complex dynamics involved. Examples of attractors and trajectories are presented. The effect of the speed of adaptation of the expected rate is also briefly discussed. Finally, we explore a special model variation incorporating the “wealth effect” which is found to behave similarly to the basic model, contrary to the model of fixed exchange rates in which incorporation of this effect causes an entirely different behavior.