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Ida and colleagues have proposed an image segmentation scheme in which a new application of fractal coding is used to iterate pixel transformations on the image plane. However, in Ida's segmentation scheme some problems remain because domains with multiple labels or indefinite boundaries are generated. In this paper, a solution to these problems is proposed, in which labeling is performed by periodic points and labels are corrected by fractal transformation. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 85(4): 66–72, 2002 [ABSTRACT FROM AUTHOR]

Local iterated function system (LIFS) image coding is currently a main topic of fractal image coding and is being studied from various points of view. However, its performance is still inferior to conventional schemes such as JPEG. This paper proposes a novel local transformation called extended condensation and reports that the LIFS coding scheme is significantly improved by combining the technique with Ida's average separation scheme. When the compression ratio is high, a better decoded image is acquired by the proposed scheme than by JPEG. © 1999 Scripta Technica, Syst Comp Jpn, 30(5): 1–8, 1999 [ABSTRACT FROM AUTHOR]

A learning algorithm is introduced for chaotic dynamical systems that solve nonlinear optimization problems. The algorithm controls the asymptotic measure of a chaotic dynamical system that searches for the optimum solution and improves the efficiency of chaotic search dynamics. Using several instances of 1- and 2-dimensional nonlinear optimization problems, the performance of the learning algorithm is demonstrated. We also show that the learning algorithm works as chaotic simulated annealing, which brings about gradual convergence of the chaotic search dynamics to a possible optimum solution. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(3): 10–21, 1999 [ABSTRACT FROM AUTHOR]

This paper discusses bifurcation diagram reconstruction [1, 2] and shows by a numerical experiment that the correct bifurcation diagram of a dynamical system can be reconstructed from the signal of a chaotic dynamical system perturbed by a sufficiently large dynamical noise. It is also verified that the predictor derived using the proposed method not only can approximate the dynamical rules on the attractor, but also has an excellent global approximation ability on a sufficiently large open set containing the attractor. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(11): 30–45, 1997 [ABSTRACT FROM AUTHOR]

Reports experimental observations of codimension-two heteroclinic bifurcations in an autonomous third-order electrical circuit. Circuit observations; One parameter bifurcations; Codimension-two bifurcations; Confirmations.

A simple algorithm is proposed for reconstruction of parametrized families of chaotic dynamics. This algorithm enables one to generate bifurcation diagrams which are qualitatively the same as the original ones only from several time-waveforms, without knowing an explicit form of the dynamics and information of the parameter values. The algorithm consists of two steps. First, globally smooth nonlinear predictors are computed for all time waveforms. Second, the Karhunen-Loéve transform is used to find only significant parameters contributing to the bifurcations. The algorithm is tested against two parametrized families of dynamics: the Hénon family and the coupled logistic/delayed-logistic family. © 1997 John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

For several chaotic time series recorded from a dynamical system with different bifurcation parameter values, Kajiwara and colleagues proposed a method (bifurcation diagram reconstruction) of reconstructing a parametrized family of nonlinear predictors which exhibits bifurcation phenomena qualitatively similar to the original [9, 10]. Based on this method, chaotic time series can be characterized by the parameter values of the nonlinear predictors. We call the characterization of chaotic time series in terms of the underlying bifurcation parameter values “recognition” of chaotic time series. In order to apply the idea to real-world systems, which are usually described by a continuous-time dynamical system and also contain observational noise, several extensions of the method are necessary. Hence, this paper presents an extended algorithm for reconstructing bifurcation diagrams of a continuous-time dynamical system in the presence of observational noise. The effectiveness of the method is demonstrated by a numerical experiment using the Rössler equation. Applicability of the bifurcation diagram reconstruction technique to the recognition of chaotic time series is also examined. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(3): 35–46, 1998 [ABSTRACT FROM AUTHOR]

This paper presents a global bifurcation scenario for chaotic dynamical systems that solve optimization problems. First, a chaotic dynamical system is constructed by a discretization of the gradient-descent dynamical system of the objective function. With an increase in the discretization parameter, local minimum solutions of the objective function bifurcate into chaotic attractors through a period-doubling bifurcation. The chaotic attractors are initially localized in the state space and eventually merge into a single global chaotic attractor via a series of crises. On the global chaotic attractor which visits a variety of local minima, “chaotic search” for a global minimum is realized. On the basis of the bifurcation scenario, we provide a guideline for tuning the bifurcation parameter value which gives rise to an efficient “chaotic search.” We also consider the efficiency of the “chaotic simulated annealing” algorithm in the light of its annealing schedule. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(2), 1–12, 1998 [ABSTRACT FROM AUTHOR]

We previously reported the chaos induced by the frustration of interaction in a nonmonotonic sequential associative memory model, and showed the chaotic behaviors at absolute zero. We have now analyzed bifurcation in a stochastic system, namely, a finite-temperature model of the nonmonotonic sequential associative memory model. We derived order-parameter equations from the stochastic microscopic equations. Two-parameter bifurcation diagrams obtained from those equations show the coexistence of attractors, which do not appear at absolute zero, and the disappearance of chaos due to the temperature effect.