Topological invariance of superconducting arrays

Noise-enhanced temporal association in neural networks

We consider a network of globally coupled neuronal oscillators subject to random force, and investigate numerically dynamic responses to external periodic driving. The order parameter, which measures the overlap between the configuration of the system and embedded patterns, is found to exhibit stochastic resonance behavior, as manifested by the signal-to-noise ratio (SNR). The optimal noise level at which the SNR reaches its maximum is found to depend on the driving frequency. On the other hand, as the randomness in the driving amplitude is increased, the system undergoes a transition from the memory-retrieval state to the mixed-memory one. The noise effects on the temporal-association state in the absence of external periodic driving are also investigated, revealing similar noise-enhanced resonance.

Phase synchronization and noise-induced resonance in systems of coupled oscillators

We study synchronization and noise-induced resonance phenomena in systems of globally coupled oscillators, each possessing finite inertia. The behavior of the order parameter, which measures the collective synchronization of the system, is investigated as the noise level and the coupling strength are varied, and hysteretic behavior is manifested. The power spectrum of the phase velocity is also examined and the quality factor as well as the response function is obtained to reveal noise-induced resonance behavior.

Synchronization in a system of globally coupled oscillators with time delay

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis of these equations reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition, between the incoherent state and a multitude of coherent states with different synchronization frequencies. In particular, the phase diagram is obtained on the plane of the coupling strength and the delay time, and ubiquity of multistability as well as suppression of the synchronization frequency is manifested. Numerical simulations are also performed to give consistent results.

Synchronization and resonance in a driven system of coupled oscillators

We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective synchronization of the system, is derived; it is found that the total order parameter decreases monotonically with noise, indicating overall suppression of synchronization. Still, for large coupling strengths, there exists an optimal noise level at which the periodic (ac) component of the order parameter reaches its maximum. The response of the phase velocity is also examined and found to display resonance behavior.