Discrete Dynamics in Nature and Society
Volume 4 (2000), Issue 4, Pages 319-331
doi:10.1155/S1026022600000303
A nonlinear macrodynamic model with fixed exchange rates: Its dynamics and noise effects
Toshichiro Asada1
, Toshio Inaba2
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
Abstract
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.