Search

We propose a new prediction method for nonlinear time series based on the paradigm of deterministic chaos. Introducing a stochastically equivalent dynamical system to an original map, a prediction method is derived by minimizing a random term that defines intervals in which a good prediction performance is obtained. The use of the present method is illustrated for some chaotic systems with particular emphasis on issues of choices of variable time steps that are necessary when discretizing the stochastic differential equation. Applying to some systems, it is found that the present method works better than traditional chaotic methods. [ABSTRACT FROM AUTHOR]

In the vicinity of the critical point of chaos as the accumulation point of period doubling bifurcations, the characteristic index is closely related to the bifurcation structure. Chaos is a typical nonlinear system, and hence its trajectory cannot be accurately reconstructed. However, qualitative evaluation is possible for the index that characterizes the vicinity of the critical point by a linear approximation model. In this paper, the lagged regression threshold model is used to quantitatively understand the characteristics of chaos, such as the Lyapunov index and the characteristic index. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(5): 1–9, 1999 [ABSTRACT FROM AUTHOR]

This paper derives a renormalization formula defined on the parameter space where mapping behavior is preserved, together with the equivalent potential function. In contrast to the universal function given by Feigenbaum, the behavior near the critical point is governed by the potential function. There are several interesting features which are shared by Feigenbaum's universal function, such as the representation of the critical point in terms of the unstable fixed point of the potential function, but the mapping differs from the scaling. The one-dimensional mapping is considered as an example, and the critical point and the scaling, which are major constants characterizing chaos from the potential function, are calculated precisely. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(8): 41–51, 1998 [ABSTRACT FROM AUTHOR]