Nonlinear Dynamics and Economic Growth

The primary aim of the project was to apply the theory of nonlinear dynamic systems to problems from economic policy and theory. The following methods were used as main basis: bifurcation theory, theory of intertemporal decision processes (control theory), and theory of dynamic games. Beside the results presented in the interim reports the following innovative aspects can be concluded: Optimal policy strategies were developed for numerous interesting problems regarding the dynamic economy, and their economic causes and consequences were investigated, as well as the dependency on model assumptions and the robustness with respect to parameter variations. Especially the complexity of optimal paths (limit cycles, multiple equilibria, indetermination, chaos) were analyzed. Thereby it was possible to gain important insights not only to the analytical and numerical methods of the bifurcation theory, but also to relations in important fields of economics and business administration. Throughout the project international cooperation were carried on with institutes from USA, CMU Pittsburgh, USC L.A., UC at Berkley, Steklov Inst. Moscow, Irkutsk State Univ., Univ. of Adelaide and Sidney, a.o. Information regarding the results and the implementations can be found in the interim reports, especially the report from 2000. There was an unexpected variety of analytical models, which was caused partly by unexpected research results, and partly by the situation with the employees. The tense situation of the job market in the field of business sciences and applied mathematics (also in combination with the payment) was an obstacle for the successful conclusion of the project. It was (and is) very difficult to get good researchers with relevant working knowledge of nonlinear dynamical systems and control theory. On the other hand it must be emphasized that the scientific output of the project was very satisfying. This statement can be proved by the quality and the number of the relevant publications. The change towards dynamical systems with distributed parameters in the last phase of the project opens an interesting approach for future research.