著者

徳永 隆治 松本 隆 徳田 功

出版者

一般社団法人日本応用数理学会

雑誌

応用数理 (ISSN:09172270)

巻号頁・発行日

vol.7, no.4, pp.271-282, 1997-12-15

被引用文献数

1

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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.