In-phase State Research Articles

Stability of the synchronized network of Hindmarsh–Rose neuronal models with nearest and global couplings

We analytically and numerically investigate a set of N identical and non-identical Hindmarsh–Rose neuronal models with nearest-neighbor and global couplings. The stability boundary of the synchronized states is analyzed using the Master Stability Function approach for the case of identical oscillators (complete synchronization) and the Kuramoto order parameter for the disordered case (phase synchronization). We find that, through a linear coupling modeling electrical synapses, complete synchronization occurs in a system of many nearest-neighbor or globally coupled identical oscillators, and in the case of non-identical neurons it is stable even in the presence of a spread of the parameters. We find that the Hindmarsh–Rose neuronal models can synchronize when coupled through the action of potential variable or through the interaction by rapid flows of ions through the membrane. The degree of connectivity of the network favors synchronization: in the global coupling case, the threshold for the in-phase state stabilizes when the number of dynamical units increases. The transition from disordered to the ordered state is a second order dynamical phase transition, although very sharp.

Selective averaging with application to phase reduction and neural control

For a class of vector fields, we show that one can selectively average terms which are of the same order in a small parameter, giving an extension of standard averaging results. Such selective averaging is illustrated for the phase reduction of a system of oscillators with both coupling and external input, for which the coupling can be averaged to give a term which only depends on phase differences, while the external input term is not averaged. For a coupled two-neuron system, we use selectively averaged equations to find the optimal input which takes the in-phase state to the anti-phase state.

Stochastic resonance in periodic potentials driven by colored noise

We studied the motion of an underdamped Brownian particle in a periodic potential subject to a harmonic excitation and a colored noise. The average input energy per period and the phase lag are calculated to quantify the phenomenon of stochastic resonance (SR). The numerical results show that most of the out-of-phase trajectories make a transition to the in-phase state as the temperature increases. And the colored noise delays the transitions between these two dynamical states. The each curve of the average input energy per period and the phase lag versus the temperature exist a mono peak and SR appears in this system. Moreover, the optimal temperature where the SR occurs becomes larger and the region of SR grows wider as the correlation time of colored noise increases.

Long-exposure far-field properties of the array of mutually-injected fiber lasers

In this paper, the long-exposure far-field properties of the array of mutually-injected fiber lasers are studied to understand the effect of the multiple phase-locked states on coherent beam combining of the array. It is found that the long-exposure far-field will degenerate into the superposition of the intensities of the elementary lasers when all the phase-locked states of the array are exported with the same probability. It means that the interference pattern will be greatly weakened in the long-exposure far-field because of the export of multiple phase-locked states of the array. This result implies that the multiple phase-locked states of the array go against coherent beam combining of the array, and only some of these phase-locked states should be exported. Then, the effects of the high-order phase-locked states on the far-field are discussed. The result suggests that only the in-phase state should be exported (i.e., all the other phase-locked states should be suppressed) in order to realize high-efficiency (>80%) coherent beam combining when the number of the elementary lasers of the array is smaller than 19.

Resonance tongues in a system of globally coupled FitzHugh–Nagumo oscillators with time-periodic coupling strength

We investigate the dynamics of a population of globally coupled FitzHugh-Nagumo oscillators with a time-periodic coupling strength. While for synchronizing global coupling, the in-phase state is always stable, the oscillators split into several cluster states for desynchronizing global coupling, most commonly in two, irrespective of the coupling strength. This confines the ability of the system to form n:m locked states considerably. The prevalence of two and four cluster states leads to large 2:1 and 4:1 subharmonic resonance regions, while at low coupling strength for a harmonic 1:1 or a superharmonic 1:m time-periodic coupling coefficient, any resonances are absent and the system exhibits nonresonant phase drifting cluster states. Furthermore, in the unforced, globally coupled system the frequency of the oscillators in a cluster state is in general lower than that of the uncoupled oscillator and strongly depends on the coupling strength. Periodic variation of the coupling strength at twice the natural frequency causes each oscillator to keep oscillating with its autonomous oscillation period.

Deformable self-propelled particles with a global coupling

We have proposed a model of deformable self-propelled particles in which the time-evolution equations are given in terms of the center-of-mass velocity and a nematic order parameter representing the motion-induced deformation [T. Ohta and T. Ohkuma, Phys. Rev. Lett. 102, 154101 (2009)]. We investigate its many-body problem applying a global orientational coupling. Depending on the strength of the interaction, the self-propelled particles exhibit various kinds of collective dynamics and chaotic behavior: a ballistic procession state, a scattered state, a coherently phase synchronized state, two types of in-phase synchronized state, and an anomalously diffusive state. The phase reduction method for the weak coupling regime reveals the bifurcations between the secular collective motions. The phase boundary among the chaos regime and the synchronized regimes is determined by the linear stability analysis of the synchronized states.

Partial Synchronization Dynamics of Coupled Ultradian Oscillators Comprising an Insect Neurosecretory Cell System

An insulin-related peptide, bombyxin, in the silkmoth Bombyx mori is secreted by four pairs of cerebral neurosecretory cells that form a weakly coupled oscillator system to produce a pulsatile pattern of hormone secretion. The activity of individual bombyxin-producing (BP) cells oscillated with different periods (20-70 min). The population of BP cells exhibited complex phase dynamics, including spontaneous synchronization and desynchronization of different combinations of cells. Statistical cross-correlation analyses of oscillation patterns between BP cells revealed that one cell usually correlated closely with a few particular cells of similar periodicity. Close investigation of the phase differences between individual active phases of the related cell pairs revealed that an inphase synchronous state was usually maintained for many cycles, whereas an antiphase state was transient, lasting for a few cycles. In contrast, antiphase synchronous states often occurred between several cell pairs when the brain containing the cerebral neurosecretory cell system was disconnected from the ventral nerve cord containing the neuronal mechanism that induced periodic heartbeat reversals at intervals of 80-110 min and exerted a periodic suppressive or phase-resetting effect on individual BP cells. These results suggest that the internal coupling mechanism in the BP cell system is not sufficient to maintain an in-phase synchronous state in the heterogeneous cell population, and that the external phase resetting mechanism may assist in-phase synchronization of many neurosecretory cells to generate an overall pulsatile pattern of bombyxin secretion.

Modeling synchronized calling behavior of Japanese tree frogs

We experimentally observed synchronized calling behavior of male Japanese tree frogs Hyla japonica; namely, while isolated single frogs called nearly periodically, a pair of interacting frogs called synchronously almost in antiphase or inphase. In this study, we propose two types of phase-oscillator models on different degrees of approximations, which can quantitatively explain the phase and frequency properties in the experiment. Moreover, it should be noted that, although the second model is obtained by fitting to the experimental data of the two synchronized states, the model can also explain the transitory dynamics in the interactive calling behavior, namely, the shift from a transient inphase state to a stable antiphase state. We also discuss the biological relevance of the estimated parameter values to calling behavior of Japanese tree frogs and the possible biological meanings of the synchronized calling behavior.

Stabilization of the in-phase fluxon state by geometrical confinement in smallBi2Sr2CaCu2O8+xmesa structures

Thein-phase (rectangular) fluxon lattice is required for achieving coherent THzemission from stacked Josephson junctions. Unfortunately, it is usually unstabledue to mutual repulsion of fluxons in ...

Effect of Gain-Dependent Phase Shift on Fiber Laser Synchronization

Recent experiments have demonstrated synchronization of fiber laser arrays at low and moderate pump levels. It has been suggested that a key dynamical process leading to synchronized behavior is the differential phase shift induced by the gain media. We explore theoretically the role of this effect in generating inphase dynamics. We find that its presence can substantially enhance the degree of inphase stability to an extent that could be practically important. At the same time, our analysis shows that a gain-dependent phase shift is not a necessary ingredient in the dynamical selection of the inphase state, thus, leading us to reconsider the essential mechanism behind inphase selection in fiber laser arrays.

Power emitted by an array of ultra high frequency current modulated semiconductor lasers with global coupling

We report the output power emitted by an array of ultra high frequency current modulated semiconductor lasers (CMSCL) whose elements are mutually coupled in a ring configuration and globally coupled through an external mirror. By varying the coupling strengths, we determine the domain where the in-phase state occurs. The dependence of the output power on the coupling strengths is analyzed. The power increases with the number of lasers and shows an abrupt increase or decrease as the coupling strengths increase. This particular behaviour is related to synchronization.

Volumetric power consumption in baffled shake flasks

For the cultivation of microorganisms, baffled shake flasks are employed when increased levels of oxygenation and mixing are required. Their use has been discouraged, however, due to the danger of a wetted sterile plug and the lower reproducibility of the experimental results. Consequently, there are only few studies dealing with this type of shaken bioreactor, and there is practically no characterization of this reactor type from a chemical engineering viewpoint. Therefore, a systematic study to elaborate the basic characteristics of the volumetric power consumption and the unfavorable out-of-phase phenomenon in baffled shake flasks is undertaken. A new type of measuring device was developed to measure the volumetric power consumption in a single shake flask. The volumetric power consumption was found to increase with increasing shaking frequency and with decreasing filling volume. Further, an independency of power consumption on the shaking diameter was observed as long as the fluid motion is in-phase. A comparison of two different baffle geometries demonstrated that deeper baffles cause more resistance to fluid flow. For the commonly employed shaking diameter of 25 mm, the investigated baffled flask types may not be operated in the in-phase state. A larger shaking diameter must therefore be employed. It was found for the first time that for all in-phase conditions, the dimensionless Newton number Ne ′ is independent of the Reynolds number Re. Power consumption in baffled shake flasks may therefore be described by a characteristic Ne ′ only dependent on the filling volume V L and the flask type. Even though there are quantitative differences, a qualitative similarity between fluid flow in stirred tanks and shake flasks has been demonstrated.

Weak-link synchronization

We describe a mutual synchronization mechanism observed in a model of fiber laser arrays. Though suboptimal in terms of total coherent power, the weak-link-synchronized state is far more robust than the in-phase state of a uniformly pumped array, with respect to parameter mismatch among the individual elements. We find similar dynamical behavior in a more general system of coupled oscillators where the amplitude dynamics is crucial.

Convection-compensating diffusion experiments with phase-sensitive double-quantum filtering

We present a design scheme for phase-sensitive, convection-compensating diffusion experiments with gradient-selected homonuclear double-quantum filtering. The scheme consists of three blocks: a 1/2 J evolution period during which antiphase single-quantum coherences are created; a period of double-quantum evolution; and another 1/2 J period, during which antiphase single-quantum coherences are converted back into an in-phase state. A single coherence transfer pathway is selected using an asymmetric set of gradient pulses, and both diffusion sensitization and convection compensation are built into the gradient coherence transfer pathway selection. Double-quantum filtering can be used either for solvent suppression or spectral editing, and we demonstrate examples of both applications. The new experiment performs well in the absence of a field-frequency lock and does not require magnitude Fourier transformation. The proposed scheme may offer advantages in diffusion measurements of spectrally crowded systems, particularly small molecules solubilized in colloidal solutions or bound to macromolecules.

Influences of synaptic location on the synchronization of rhythmic bursting neurons

We study how the location of synaptic input influences the stablex firing states in coupled model neurons bursting rhythmically at the gamma frequencies (20-70 Hz). The model neuron consists of two compartments and generates one, two, three or four spikes in each burst depending on the intensity of input current and the maximum conductance of M-type potassium current. If the somata are connected by reciprocal excitatory synapses, we find strong correlations between the changes in the bursting mode and those in the stable phase-locked states of the coupled neurons. The stability of the in-phase phase-locked state (synchronously firing state) tends to change when the individual neurons change their bursting patterns. If, however, the synaptic connections are terminated on the dendritic compartments, no such correlated changes occur. In this case, the coupled bursting neurons do not show the in-phase phase-locked state in any bursting mode. These results indicate that synchronization behaviour of bursting neurons significantly depends on the synaptic location, unlike a coupled system of regular spiking neurons.

Influences of synaptic location on the synchronization of rhythmic bursting neurons

We study how the location of synaptic input influences the stablex firing states in coupled model neurons bursting rhythmically at the gamma frequencies (20–70 Hz). The model neuron consists of two compartments and generates one, two, three or four spikes in each burst depending on the intensity of input current and the maximum conductance of M-type potassium current. If the somata are connected by reciprocal excitatory synapses, we find strong correlations between the changes in the bursting mode and those in the stable phase-locked states of the coupled neurons. The stability of the in-phase phase-locked state (synchronously firing state) tends to change when the individual neurons change their bursting patterns. If, however, the synaptic connections are terminated on the dendritic compartments, no such correlated changes occur. In this case, the coupled bursting neurons do not show the in-phase phase-locked state in any bursting mode. These results indicate that synchronization behaviour of bursting neurons significantly depends on the synaptic location, unlike a coupled system of regular spiking neurons.

Chaotic bursting as chaotic itinerancy in coupled neural oscillators

We show that chaotic bursting activity observed in coupled neural oscillators is a kind of chaotic itinerancy. In neuronal systems with phase deformation along the trajectory, diffusive coupling induces a dephasing effect. Because of this effect, an antiphase synchronized solution is stable for weak coupling, while an in-phase solution is stable for very strong coupling. For intermediate coupling, a chaotic bursting activity is generated. It is a mixture of three different states: an antiphase firing state, an in-phase firing state, and a nonfiring resting state. As we construct numerically the deformed torus manifold underlying the chaotic bursting state, it is shown that the three unstable states are connected to give rise to a global chaotic itinerancy structure. Thus we claim that chaotic itinerancy provides an alternative route to chaos via torus breakdown.

Self-organization in a multicore fiber laser array

We explain an observed spontaneous transition to the high-brightness, in-phase array state of a seven-core ytterbium-doped fiber laser array [IEEE Photonics Technol. Lett. 13, 439 (2001)]. The responsible mechanism is nonlinear refraction, and either in-phase or antiphase array modes can be selected by control of pump intensity. The phenomenon appears to be robust and scalable.

Phase Locking States in Network of Inhibitory Neurons: A Putative Role of Gap Junction

Recent experiments revealed that the neocortical inhibitory neurons, which are believed to play a crucial role in controlling the cortical coherent activity, are coupled not only with the conventional synapses but also with gap junctions. In this letter, we study the synchronization properties in the network of Hodgkin–Huxley neurons coupled with both conventional chemical synapses and gap junctions, and explore the putative functional role of the gap junctions. In general, gap junction coupling is modeled as producing currents proportional to the differences in the membrane voltages between the two neurons. Usually, it is expected that the diffusive form of this coupling leads to synchronization of two neurons. However, as a result of phase oscillator analysis, we found that, in the two-neuron network, the gap junction stabilizes not only the in-phase state but also the antiphase one. Furthermore, in the population of inhibitory neurons, we numerically demonstrate that if the strength of the gap junction...

Synchronizability of distributed clock oscillators

We analyze the synchronizability of synchronous distributed oscillators (SDOs), a novel clocking scheme for microprocessors. A computer-aided perturbation analysis is developed for such systems, where analytically tractable equations of the clock phases are reduced from experimental data reflecting all circuit details. Using this reduction, a theory is constructed to explain the underlying mechanism of the synchronization in SDOs. It systematically explains the observed phenomena, the existence and stability of the (mutually) synchronized states, and the transition from the in-phase synchronized state to the out-of-phase (but still synchronized) state. Furthermore, the present theory of phase reduction provides a new design principle of coupled oscillators based on "the equation"; a precise delay control (less than the gate delay) circuit can be designed in a simple and general form.