| Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 15, Iss. 1, Jan, 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 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 |