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.Comment: 17 pages, 3 figure

Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises

Dynamics of an ensemble of $N$-unit FitzHugh-Nagumo (FN) neurons subject to white noises has been studied by using a semi-analytical dynamical mean-field (DMF) theory in which the original $2 N$-dimensional {\it stochastic} differential equations are replaced by 8-dimensional {\it deterministic} differential equations expressed in terms of moments of local and global variables. Our DMF theory, which assumes weak noises and the Gaussian distribution of state variables, goes beyond weak couplings among constituent neurons. By using the expression for the firing probability due to an applied single spike, we have discussed effects of noises, synaptic couplings and the size of the ensemble on the spike timing precision, which is shown to be improved by increasing the size of the neuron ensemble, even when there are no couplings among neurons. When the coupling is introduced, neurons in ensembles respond to an input spike with a partial synchronization. DMF theory is extended to a large cluster which can be divided into multiple sub-clusters according to their functions. A model calculation has shown that when the noise intensity is moderate, the spike propagation with a fairly precise timing is possible among noisy sub-clusters with feed-forward couplings, as in the synfire chain. Results calculated by our DMF theory are nicely compared to those obtained by direct simulations. A comparison of DMF theory with the conventional moment method is also discussed.Comment: 29 pages, 2 figures; augmented the text and added Appendice

Different effects of L-arginine on morphine tolerance in sham and ovariectomized female mice*

Objective: The roles of gonadal hormones and nitric oxide (NO) on the analgesic effects of morphine, tolerance to morphine, and their interactions have been widely investigated. In the present study, the effect of L-arginine (an NO precursor) on morphine tolerance in sham and ovariectomized (OVX) female mice was investigated. Methods: Forty mice were divided into sham and OVX groups. On the first day, a hot plate test ((55±0.2) °C; cut-off 30 s) was carried out as a base record 15 min before injection of morphine (10 mg/kg, subcutaneously (s.c.)) and was repeated every 15 min after injection. The sham group was then divided into two subgroups: sham-tolerance-L-arginine (Sham-Tol-LA) and sham-tolerance-saline (Sham-Tol-Sal) which received either L-arginine 50 mg/kg (intraperitoneally (i.p.)) or saline 10 ml/kg (i.p.), respectively, three times in a day for three consecutive days. Morphine tolerance was induced in animals by injecting 30 mg/kg morphine (s.c.) three times/day for three days. This treatment was also used for OVX subgroups. On the fifth day, the hot plate test was repeated. The analgesic effect of morphine was calculated as the maximal percent effect (MPE). The results were compared using repeated measure analysis of variance (ANOVA). Results: There was no significant difference in MPE between the OVX and sham groups. The MPEs in both the Sham-Tol-Sal and OVX-Tol-Sal groups were lower than those in both the sham and OVX groups (P<0.01). The MPE in the OVX-Tol-Sal group was greater than that in the Sham-Tol-Sal group (P<0.01). The MPE in the Sham-Tol-LA group was higher than that in the Sham-Tol-Sal group (P<0.01). However, there was no significant difference between the Sham-Tol-LA and sham groups or between the OVX-Tol-LA and OVX-Tol-Sal groups. Conclusions: The results of the present study showed that repeated administration of morphine causes tolerance to the analgesic effect of morphine. L-Arginine could prevent tolerance to morphine but its effect was different in the presence of ovarian hormones