分岐図再構成 : 時系列信号からの係数族推定(<特集>力学系理論-応用数理における新しい展開)

概要

論文の詳細を見る
This paper reports a simple algorithm for reconstructing bifurcation diagrams only from time-wave forms of a parameterized family of dynamical systems, without knowing an explicit form of the dynamics and its dependence on the parameters. The algorithm consists of two steps. First, nonlinear predictors are sought using a particular class of nonlinear functions with a lot of model parameters. Second, significant parameters contributing the bifurcation are found by the principal component analysis. Using the parameterized family of nonlinear predictors, it is possible to obtain bifurcation diagram qualitatively similar to that of the original systems. The algorithm is tested against Henon equation and Rossler equation.
日本応用数理学会の論文
1997-12-15