Ryuji Tokunaga

A SIMPLE GEOMETRICAL STRUCTURE UNDERLYING SPEECH SIGNALS OF THE JAPANESE VOWEL /a/

An automatic milking machine is described which includes a pneumatic circuit for controlling the same and apparatus for automatically cleansing the interior of a cow milking teat cup cluster between the milking of successive cows therewith. The cleansing apparatus includes an arrangement for automatically disconnecting the teat cup cluster from the milk circuit between cows, and then successively passing therethrough various liquids which cleanse the same.

Reconstructing bifurcation diagrams only from time-waveforms

Abstract A simple algorithm is proposed for “reconstructing” bifurcation diagrams only from time-waveforms of a dynamical system, without knowing an explicit form of the dynamics and its dependence on the parameters. Reconstruction means that the obtained bifurcation diagram is qualitatively similar to that of the original system. The algorithm consists of two steps. First, a nonlinear predictor is sought using a particular class of functions with many parameters. Second, the Karhunen-Loeve transform is used to find only significant parameters contributing the bifurcations. The algorithm is tested against two families of dynamical system: the Henon family and the coupled logistic/delayed-logistic family.

Recognizing chaotic time-waveforms in terms of a parametrized family of nonlinear predictors

Abstract Consider a chaotic dynamical system which exhibits a variety of chaotic time-waveforms with a change in the bifurcation parameters. This paper presents an algorithm for estimating the underlying bifurcation parameters of the chaotic time-waveforms in experimental situation in which no a priori analytical knowledge of the dynamical system is available. First, we construct “qualitatively similar” parametrized family of nonlinear predictors only from several sets of chaotic time-waveforms. “Qualitatively similar” parametrized family means that the family of nonlinear predictors exhibits “qualitatively similar” bifurcation phenomena as the original. Chaotic time-waveforms are then characterized in terms of the “qualitatively similar” bifurcation parameters of the nonlinear predictors. We call the characterization of chaotic time-waveforms in terms of the underlying bifurcation parameters “chaotic time-waveform recognition”. Several numerical experiments using the Rossler equations show the efficiency of the algorithm. The effect of observational noise included in chaotic time-waveforms is also considered.

Back-propagation learning of infinite-dimensional dynamical systems

This paper presents numerical studies of applying back-propagation learning to a delayed recurrent neural network (DRNN). The DRNN is a continuous-time recurrent neural network having time delayed feedbacks and the back-propagation learning is to teach spatio-temporal dynamics to the DRNN. Since the time-delays make the dynamics of the DRNN infinite-dimensional, the learning algorithm and the learning capability of the DRNN are different from those of the ordinary recurrent neural network (ORNN) having no time-delays. First, two types of learning algorithms are developed for a class of DRNNs. Then, using chaotic signals generated from the Mackey-Glass equation and the Rössler equations, learning capability of the DRNN is examined. Comparing the learning algorithms, learning capability, and robustness against noise of the DRNN with those of the ORNN and time delay neural network, advantages as well as disadvantages of the DRNN are investigated.

Bifurcation analysis in an associative memory model

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.

Low-dimensional chaos induced by frustration in a non-monotonic system

We report a novel mechanism for the occurrence of chaos at the macroscopic level induced by the frustration of interaction, namely frustration-induced chaos, in a non-monotonic sequential associative memory model. We succeed in deriving exact macroscopic dynamical equations from the microscopic dynamics in the case of the thermodynamic limit and prove that two order parameters dominate this large-degree-of-freedom system. Two-parameter bifurcation diagrams are obtained from the order parameter equations. Then we analytically show that chaos is low-dimensional at the macroscopic level when the system has some degree of frustration, but that chaos definitely does not occur without frustration.

Detecting switch dynamics in chaotic time-waveform using a parametrized family of nonlinear predictors

Abstract An algorithm is presented for detecting switch dynamics in chaotic time-waveform. By the “switch dynamics,” we mean that the chaotic time-waveform is measured from a dynamical system whose bifurcation parameters are occasionally switched among a set of slightly different parameter values. First, the switched chaotic time-waveform is divided into windows of short-term time-waveforms. From the set of windowed time-waveforms, “qualitatively similar” parametrized family of nonlinear predictors is constructed. “Qualitatively similar” parametrized family means that the family of nonlinear predictors exhibits “qualitatively similar” bifurcation phenomena as the original. By characterizing the windows of short-term chaotic time-waveforms in terms of the “qualitative” parameters of nonlinear predictors, switch dynamics of their associated bifurcation parameters are detected. For the Lorenz equations, the Rossler equations, and the Mackey–Glass equations, efficiency of the algorithm is demonstrated. In the experiment, chaotic time-waveforms contaminated with observational noise is considered.

Improving LIFS image coding via extended condensations

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 Idas average separation scheme. When the compression ratio is high, a better decoded image is acquired by the proposed scheme than by JPEG.

Back-propagation learning of an infinite-dimensional dynamical system

A delay-differential equational model of recurrent neural network, the feedback connections of which are adopted by the backpropagation learning algorithm, is introduced. In contrast with the conventional recursive-ordinary-differential neural networks, which have been reported to be capable of learning complex dynamics only when enough observable dimensions of the target dynamical systems are available, our proposed delay-differential equational model acquires a diversity of time-continuous motions that are observed as an one-dimensional single time series. The system capability is demonstrated through practical experiments.

Observing a codimension‐two heteroclinic bifurcation

This paper reports experimental observations of codimension-two heteroclinic bifurcations in an autonomous third-order electrical circuit. The paper also reports confirmations by computer simulations. In the laboratory experiments, a pair of programmable resistors are used in order to adjust two bifurcation parameters. In the associated two-parameter space, several codimension-one bifurcation sets are experimentally measured to capture codimension-two bifurcation structures. All of these bifurcation sets are numerically confirmed by exact bifurcation equations which are derived from piecewise-linear circuit dynamics.