A generalized radial basis function network consisting of (1 + cosh x)-1 as the basis function of the same class as Gaussian functions is investigated in terms of the feasibility of analog-hardware implementation. A simple way of hardware-implementing (1 + cosh x)-1 is proposed to generate the exact input-output response curve on an analog circuit constructed with bipolar transistors. To demonstrate that networks consisting of the basis function proposed actually work, the networks are applied to numerical experiments of forecasting chaotic time series contaminated with observational random noise. Stochastic gradient descent is used as learning rule. The networks are capable of learning and making short-term forecasts about the dynamic behavior of the time series with comparable performance to Gaussian radial basis function networks.

We have applied the open-plus-closed-loop control method, recently devised by Grosu et al., to chaos-based communications. In our method, a message is handled as if it were part of a parameter mismatch between the chaotic oscillators installed on a drive and a response system. In the drive system, the message is encrypted by adding it to a state variable of the oscillator as dynamical noise. In the response system, the message is decrypted by subtracting the chaotic signal reproduced by chaotic synchronization using the open-plus-closed-loop control method from the received signal, followed by differentiation with respect to time. When the oscillators have multiple parameter mismatches, multiple messages can be simultaneously encrypted and decrypted to achieve multiplex secure communications.

We developed a method for extracting feature patterns from multivariate data using a network of coupled phase oscillators subject to an analogue of the Kuramoto model for collective synchronization. Our method may be called data synchronization. We applied data synchronization to the care-needs-certification data, provided by Otsu City as a historical old city near Kyoto City, in the Japanese public long-term care insurance program to find the trend of the major patterns of the aging process for elderly people needing nursing care.

We have recently developed a method for feature extraction from multivariate data using an analogue of Kuramoto's dynamics for modeling collective synchronization in a network of coupled phase oscillators. In our method, which we call data synchronization, phase oscillators carrying multivariate data in their natural and updated rhythms achieve partial synchronizations. Their common rhythms are interpreted as the template vectors representing the general features of the data set. In this study, we discuss the link of data synchronization to the self-organizing map algorithm as a popular method for data mining and show through numerical experiments how our method can overcome the disadvantages of the self-organizing map algorithm in that unintentional selections of inappropriate reference vectors lead to false feature patterns.