Discrete Dynamics in Nature and Society
Volume 4 (2000), Issue 4, Pages 319-331

A nonlinear macrodynamic model with fixed exchange rates: Its dynamics and noise effects

Toichiro Asada,1 Toichio Inaba,2 and Tetsuya Misawa3

1Faculty of Economics, Chuo University, 742-1, Higashinakano, Hachioji, Tokyo 192-0393, Japan
2School of Education, Waseda University, 1-6-1, Nishiwaseda, Shinjuku-ku, Tokyo 169-0051, Japan
3Faculty of Economics, Nagoya City University, Mizuho-cho, Mizuho-ku, Nagoya 467-0001, Japan

Received 21 October 1998; Revised 20 June 1999

Copyright © 2000 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.


In this paper, we formulate a discrete time version of the Kaldorian macrodynamic model in a small open economy with fixed exchange rates. The model is described by a system of the three-dimensional nonlinear difference equations with and without stochastic disturbances (noise effects). We study the local stability/instability properties analytically by using the linear approximation method, and chaotic dynamics with and without noise effects are investigated by means of numerical simulations. In general, it is believed that the effect of the noise is to obscure the basic structure of the system. But, this is not necessarily the case. We show by means of numerical analysis that the noise can reveal the hidden structure of the model contrary to the usual intuition in some situations.