Research on Business Cycles by Chaos Theory

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In the field of economic dynamics, the application of dynamical systems has been popular since the begining of 1980's. In the end of 1980's the emphasis was shifted to nonlinear dynamics, in particular chaos theory.By the use of non-linear dynamics, complex economic phenomenons may be explained by a relatively simple model. The purpose of this research is to establish the endogenous theories of business cycles, fertility changes and stock price changes.At the start of this project, I presented a paper on the survey of the literature in the international conference on Economic Dynamics held at Thecnical University of Vienna in Austria, May, 1995. In July I organized the workshop on endogenous growth at Otaru University of Commerce. In January, 1996, I attended the conference on International trade held in Hakone and exchanged information. By then I have collected the emprical date and I was ready to refine the model and start analysis. The survey paper with Gerhard Sorger was accepted by Journal of Nonlinear Dynamics and Econometrics.In 1996, while I started to build the macro economic model and investigate its mathematical properties, I discussed with mathermaticians, engineers and foreign researchers. I visited Cornell University in May, Institute of Mathematics (IMPA) in Brasil in August, New York University in November and presented ongoing research and exchenged information. As a result, in the new macro dynamic model with increasing returns, I obtained conditions for economic growth, business cycles and chaos and could analyze dynamics of growth paths by computer simulations. I am now writing those results as a paper to submit to an international journal.