As a new method for data synchronization, a modified version of the Kuramoto model is introduced to solve the clustering problems. The modified model can generate data clusters with various statistical disributions by setting the natural frequencies of the oscillators to the node degrees of a complex network conveying information on multivariate data. Unlike the original method of data synchronization, the proposed method allows us to deal with a dataset having clusters with non-convex shapes. Through three case studies, we show that the proposed method outperforms existing data-clustering algorithms, such as the Density-Based Spatial Clustering of Applications with Noise.

This paper investigates the dynamical behavior of a power system for managing several energy storages, where each storage acts as a self-excited oscillator. The use of these storages is determined by the power price which is proportional to the past total power flow from a power grid to all storages. This system behaves as oscillators coupled by a time-delay global-repulsive connection. We show that multi-phase synchronization in this system can reduce the peak total power flow. A procedure for designing the system parameters so as to induce the desired multi-phase synchronization is provided. In addition, a strategy for maintaining multi-phase synchronization is proposed for use in practical situations, where some storages are added or removed from the synchronized storages. The effectiveness of the power system is demonstrated with numerical simulations.

In this study, we theoretically investigate both propagating and standing wave phenomena in five mutually-coupled bistable oscillators. The bistable oscillator is considered as a form of a Van der Pol oscillator with higher order nonlinearity. For the resonant case, the explicit forms of several propagating and standing waves are obtained using the averaging method. The associated numerical results for the weakly nonlinear oscillators are confirmed to be consistent with the theoretical results. Further, we show that a more localized propagating wave in space and time exists numerically as compared with the theoretically obtained propagating wave for strongly nonlinear oscillators.

Quantum-dot and ion-trap technologies are applied to implementation of quantum computers. Quantum mechanical systems constructed by the technologies are considered as networks of charged particles. In this paper, we present first that the networks are described by coupled quantum parametric harmonic oscillators (CQPHOs). Second, the CQPHOs are modeled by a system of nonlinear stochastic ordinary differential equations (NSODEs). The NSODEs consist of a deterministic drift term and a probabilistic fluctuation term. The drift term is derived by substituting a quantum probability density function and a quantum current density for the classical counterparts in a drift term of the Fokker-Planck equation. Third, we integrate numerically the system of the NSODEs from which probabilistic fluctuation term is removed. As a result of the integral, we find that the system behaves chaotically when the amplitude and the frequency of the time-varying parameter of the CQPHOs are in specific ranges. This implies that quantum computers may behave irregularly because not only of intrinsic probabilistic nature of quantum mechanics but also of deterministically chaotic nature.

Multi-armed bandit problems concern decision making when selecting a slot machine among many slot machines with initially uncertain hit probabilities to maximize the total reward; this is a fundamental problem of reinforcement learning. Furthermore, competitive multi-armed bandit problems involve multiple agents in play, manifesting fundamental concerns regarding social figures, not just individual rewards. A representative issue is selection conflict, in which multiple players select the same slot machine and may miss the total reward as a whole. This study proposes a scheme for solving the competitive multi-armed bandit problem using semiconductor laser networks by introducing an exclusive selection mechanism. We numerically implement our method and compare it with conventional algorithms. We show that our method outperforms conventional algorithms in solving the competitive multi-armed bandit problem.