Study on Structures and Dynamics of Nonlinear Systems

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With the rapid advance of VLSI and the discovery of new nonlinear phenomena such as soliton and chaos, analysis of nonlinear dynamic systems becomes very important. The purpose of this project is to clarify the fundamental properties of both the nonlinear system structure and its dynamics, and to buid the foundation of their applications to the practical problems, by means of the new mathematical methods which the present researchers have developed.This project has been accomplished over three years, and its fruitful result is establishment and mutual recomposition of the following theories :1. Theory on evaluation of the overall dependence on internal structures and parameters of nonlinear systems, by making use of the original theory of nondeterministic operators.2. Theory on numerical analysis of nonlinear systems by the original methods based on homotopy or decomposition.3. New approach for the analysis of nonlinear phenomena such as soliton and chaos. Furthermore, using the above theories, we threw light on the followings :4. Observation of a non-periodic attractor from an extremely simple circuit, and the rigorous proof of the attractor to be chaotic.5. Modelling of parallel blower and multibody systems and analysis of their dynamics.6. Analysis of the models of optical transmission and biological systems.