Studies on Modeling and Performance Analysis of Nonlinear Dynamic Systems

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This scientific research has been done during the period from May, 1988 to March 1981. The purpose of the research is to do systematic research on modeling and performance analysis of nonliear dynamic systems. The following are main results obtained by the research :1. Analysis of Fluctuation of Nonlinear Dynamic Systems and Studies on Infinite Dimensional Homotopy MethodA number of properties have been clarified on response of fluctuations to nonlinear systems by developing a theory of non-deterministic operators. Moreover, an infinite dimensional homotopy method has been established for numerically analyzing nonlinear systems including infinite dimensional systems.2. Local and Global Bifurcation Phenomena of Nonlinear CircuitsA number of properties have been clarified on the global bifurcation phenomena in nonlinear circuits analysis. Moreover, a number of interesting bifurcation phenomena have been observed by computer simulations and circuit experiments.3. Numerical Method of Nonlinear Dynamic SystemsAn efficient algorithm has been developed for caluculating solutions of nonlinear circuits, nonlinear programming, channels, and all solutions of a certain class of nonlinear equations.4. Modelig of Dynamical Systems and Its ApplicationBy using concept of the bond graph an automatic modeling method is presented for a class of dynamical systems. Based on this, an efficient modeling and a numerical integral method have been established for analyzing flexible multibody dynamics.