Study on a relationship between nonlinear dynamical system and stochastic model

In this paper, a relationship between nonlinear dynamical system and statistical model is considered, and it is clarified that a second order nonlinear dynamical system is approximated by a Bi-variate Time Varying AutoRegressive (BTVAR) model with respect to a displacement or a rotation angle component and a velocity or a angular velocity component which is a kind of time series models.This obtained finding is applied to a stability judgment system of ships. That is, to monitor characteristic roots of the characteristic equation associated with a BTVAR operator online, the judgment for stability of ships is carried out. In this case, BTVAR coefficients are estimated by using an algorism of Kalman Filter. The verification of this idea is carried out based on numerical experiments. From the comparison of the proposed procedure and a Scalar Time Varying AutoRegressive (SVAR) modeling procedure with respect to a goodness of fit to the data of the model based on Akaike Information Criterion (AIC), it is confirmed that the proposed procedure is better than the SVAR modeling procedure from the view point of AIC.