Isao Nishikawa

Center manifold reduction for large populations of globally coupled phase oscillators.

A bifurcation theory for a system of globally coupled phase oscillators is developed based on the theory of rigged Hilbert spaces. It is shown that there exists a finite-dimensional center manifold on a space of generalized functions. The dynamics on the manifold is derived for any coupling functions. When the coupling function is sin θ, a bifurcation diagram conjectured by Kuramoto is rigorously obtained. When it is not sin θ, a new type of bifurcation phenomenon is found due to the discontinuity of the projection operator to the center subspace.

Sustainable ITS project overview: mixed reality traffic experiment space under interactive traffic environment for ITS

In this paper, we show the outline of our research on interactive traffic environment, under which we are developing mixed reality traffic experiment space. In order to develop sophisticated ITS applications, it is very important to analyze human factor, but there is few method to obtain human factor, thus, we have decided to create interactive traffic environment under which we can obtain human factors. As the first stage of our research, we have developed mixed reality traffic experiment space. It consists of real observation laboratory part and virtual experiment laboratory part. In the former part, we gather various real raw data to retrieve real environment model. In the later part, we present users more realistic driving environment based on the model. Based on this experiment space, we are going to proceed to the next stages, in which we design and evaluate sustainable ITS applications. For this purpose we have started sustainable ITS project at the university of Tokyo, collaborated among industry, government, and university.

Long-term fluctuations in globally coupled phase oscillators with general coupling: Finite size effects

We investigate the diffusion coefficient of the time integral of the Kuramoto order parameter in globally coupled nonidentical phase oscillators. This coefficient represents the deviation of the time integral of the order parameter from its mean value on the sample average. In other words, this coefficient characterizes long-term fluctuations of the order parameter. For a system of N coupled oscillators, we introduce a statistical quantity D, which denotes the product of N and the diffusion coefficient. We study the scaling law of D with respect to the system size N. In other well-known models such as the Ising model, the scaling property of D is D∼O(1) for both coherent and incoherent regimes except for the transition point. In contrast, in the globally coupled phase oscillators, the scaling law of D is different for the coherent and incoherent regimes: D∼O(1/N(a)) with a certain constant a>0 in the coherent regime and D∼O(1) in the incoherent regime. We demonstrate that these scaling laws hold for several representative coupling schemes.

Finite-size scaling in globally coupled phase oscillators with a general coupling scheme

We investigate a critical exponent related to synchronization transition in globally coupled nonidentical phase oscillators. The critical exponents of susceptibility, correlation time, and correlation size are significant quantities to characterize fluctuations in coupled oscillator systems of large but finite size and understand a universal property of synchronization. These exponents have been identified for the sinusoidal coupling but not fully studied for other coupling schemes. Herein, for a general coupling function including a negative second harmonic term in addition to the sinusoidal term, we numerically estimate the critical exponent of the correlation size, denoted by

研究速報 : A simulation model for evaluation of merging capacity on the Metropolitan Expressway

\nu_+

Construction of a Data Set for Validation of Traffic Simulations

, in a synchronized regime of the system by employing a non-conventional statistical quantity. First, we confirm that the estimated value of

Phase-Model Analysis of Supply Stability in Power Grid of Eastern Japan

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Switching phenomenon induced by breakdown of chaotic phase synchronization

is approximately 5/2 for the sinusoidal coupling case, which is consistent with the well-known theoretical result. Second, we show that the value of

Nonstandard scaling law of fluctuations in finite-size systems of globally coupled oscillators.

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IMPROVING THE CONTROL STRATEGIES OF FREEWAY MERGING POINTS USING MODELING AND SIMULATION APPROACH

increases with an increase in the strength of the second harmonic term. Our result implies that the critical exponent characterizing synchronization transition largely depends on the coupling function.