Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 15, Iss. 1, January, 2011, pp. 105-128
@2011 Society for Chaos Theory in Psychology & Life Sciences


Numerical Exploration of Kaldorian Interregional Macrodynamics: Stability and the Trade Threshold for Business Cycles Under Fixed Exchange Rates

Toichiro Asada, Faculty of Economics, Chuo University, Tokyo
Christos Douskos, Faculty of Engineering, University of Patras, Greece
Panagiotis Markellos, Faculty of Engineering, University of Patras, Greece

Abstract: The stability of equilibrium and the possibility of generation of business cycles in a discrete interregional Kaldorian macrodynamic model with fixed exchange rates are explored using numerical methods. One of the aims is to illustrate the feasibility and effectiveness of the numerical approach for dynamical systems of moderately high dimensionality and several parameters. The model considered is five-dimensional with four parameters, the speeds of adjustment of the goods markets and the degrees of economic interactions between the regions through trade and capital movement. Using a grid search method for the determination of the region of stability of equilibrium in two-dimensional parameter subspaces, and coefficient criteria for the flip bifurcation - and Hopf bifurcation - curve, we determine the stability region in several parameter ranges and identify Hopf bifurcation curves when they exist. It is found that interregional cycles emerge only for sufficient interregional trade. The relevant threshold is predicted by the model at 14 - 16 % of trade transactions. By contrast, no minimum level of capital mobility exists in a global sense as a requirement for the emergence of interregional cycles; the main conclusion being, therefore, that cycles may occur for very low levels of capital mobility if trade is sufficient. Examples of bifurcation and Lyapunov exponent diagrams illustrating the occurrence of cycles or period doubling, and examples of the development of the occurring cycles, are given. Both supercritical and subcritical bifurcations are found to occur, the latter type indicating coexistence of a point and a cyclical attractor.

Keywords: Hopf-Neimark bifurcation, business cycles, international trade