Takashi Ichinomiya

Frequency synchronization in a random oscillator network.

We study the frequency synchronization of a randomly coupled oscillators. By analyzing the continuum limit, we obtain a sufficient condition for the mean-field-type synchronization. We especially find that the critical coupling constant K becomes 0 in the random scale-free network, P(k) proportional, variant k(-gamma), if 2<gamma</=3. Numerical simulations in finite networks are consistent with this analysis.

Path-integral approach to dynamics in a sparse random network

We study the dynamics involved in a sparse random network model. We extend the standard mean-field approximation for the dynamics of a random network by employing the path-integral approach. The result indicates that the distribution of the variable is essentially identical to that obtained from globally coupled oscillators with random Gaussian interaction. We present the results of a numerical simulation of the Kuramoto transition in a random network, which is found to be consistent with this analysis.

Persistent homology analysis of craze formation

We apply a persistent homology analysis to investigate the behavior of nanovoids during the crazing process of glassy polymers. We carry out a coarse-grained molecular dynamics simulation of the uniaxial deformation of an amorphous polymer and analyze the results with persistent homology. Persistent homology reveals the void coalescence during craze formation, and the results suggest that the yielding process is regarded as the percolation of nanovoids created by deformation.

Power-law distribution in Japanese racetrack betting

Gambling is one of the basic economic activities that humans indulge in. An investigation of gambling activities provides deep insights into the economic actions of people and sheds lights on the study of econophysics. In this paper we present an analysis of the distribution of the final odds of the races organized by the Japan Racing Association. The distribution of the final odds Po(x) indicates a clear power-law Po(x)∝1/x, where x represents the final odds. This power-law can be explained on the basis of the assumption that every bettor bets his money on the horse that appears to be the strongest in a race.

Power-law exponent of the Bouchaud-M\'ezard model on regular random network

We study the Bouchaud-Mézard model on a regular random network. By assuming adiabaticity and independency, and utilizing the generalized central limit theorem and the Tauberian theorem, we derive an equation that determines the exponent of the probability distribution function of the wealth as x→∞. The analysis shows that the exponent can be smaller than 2, while a mean-field analysis always gives the exponent as being larger than 2. The results of our analysis are shown to be in good agreement with those of the numerical simulations.

Numerical Analysis of FitzHugh-Nagumo Neurons on Random Networks

We investigate a model of randomly copuled neurons. The elements are FitzHgh-Nagumo excitable neurons. The interactions between them are the mixture of excitatory and inhibitory. When all interactions are excitatory, a rest state is globally stable due to the excitability of neurons. Increasing the number of inhibitory connections, we observe the phase transition from the rest state to an oscillatory state. An analytical description for the critical point of the transition is obtained by means of random matrix theories for an infinite number of neurons, and the result is in good agreement with numerical simulation.

Bifurcation Study of the Kuramoto Transition in Random Oscillator Networks

We study the frequency synchronization of phase oscillators in random networks. We investigate the kinetic equations of the oscillator distribution function using the continuum approximation. From a linear analysis of this model, we find that the unstable eigenfunction is proportional to k. We also derive an amplitude equation of the unstable modes employing center manifold reduction. We find that the coefficients of the Taylor expansion of the amplitude equation always diverge for random scale-free networks. The results of numerical studies are consistent with these analyses.

Thermodynamic characterization of synchronization-optimized oscillator networks.

We consider a canonical ensemble of synchronization-optimized networks of identical oscillators under external noise. By performing a Markov chain Monte Carlo simulation using the Kirchhoff index, i.e., the sum of the inverse eigenvalues of the Laplacian matrix (as a graph Hamiltonian of the network), we construct more than 1,000 different synchronization-optimized networks. We then show that the transition from star to core-periphery structure depends on the connectivity of the network, and is characterized by the node degree variance of the synchronization-optimized ensemble. We find that thermodynamic properties such as heat capacity show anomalies for sparse networks.

Bifurcation Study of Kuramoto Transition of Random Oscillator Network

We study the Kuramoto transition of oscillators in random network and Barabashi-Albert network model. In both cases, the results of numerical simulation show good coincidence with the mean-field analysis.