動径基底関数ネットワークを用いた双峰写像のリアプノフ指数推定

概要

論文の詳細を見る
Ther are many measures to characterize deterministic chaos, for instance, fractal dimensions, Lyapunov exponents, and nonlinear prediction etc. Among them, nonlinear prediction is recognized as a promising method of chaotic timeseries analysis in many fields. We can apply it to timeseries in order to analyse orbital instability and long-term unpredictability, the fundamental characteristics of deterministic chaos. In this paper, we introduce an approximation technique of nonlinear maps using radial basis function networks (RBFN), and estimate Lyapunov exponents with approximated nonlinear maps. As nonlinear mapping, we analyse a chaotic neuron model which is a bimodal mapping, since it is likely that a bimodal mapping has an important and essential role in function of our brains. We evaluate the performances of approximation by estimating Lyapunov exponents of timeseries produced from the chaotic neuron model using smoothing RBI method in the existence of noise in order to simulate the situations similar to real data analysis.
社団法人電子情報通信学会の論文
1995-09-05