External synchronization of oscillating pulse edge on a transmission line with regularly spaced tunnel diodes.

We investigate the external synchronization of the oscillating pulse edges developed in a transmission line periodically loaded with tunnel diodes (TDs), termed a TD line. It is observed that the pulse edge oscillates on a TD line when supplied by an appropriate voltage at the end of the line. We discuss how the pulse edge oscillates on a TD line and the properties of the external synchronization of the edge oscillation driven by a sinusoidal perturbation. By applying a phase-reduction scheme to the transmission equation of a TD line, we obtain the phase sensitivity, which satisfactory explains the measured spatial dependence of the locking range on the frequency. Moreover, we successfully detect the spatiotemporal behaviors of the edge oscillation by establishing synchronization with the sampling trigger of an oscilloscope.

Control of noise-induced coherent behaviors in an array of excitable elements by time-delayed feedback.

We investigate feedback-controlled coherent dynamics in a two-dimensional array of excitable elements. We demonstrate that one can freely enhance or reduce the spatiotemporal coherence of noise-induced oscillation, such as coherence resonance and phase synchronization, by controlling both the delay time and the feedback gain. Furthermore, we find that noise-induced oscillations are entrained by the feedback force in a certain range of the delay time. Experimental observations are approximately reproduced in a numerical simulation with a forced Oregonator model.

Feedback-controlled dynamics in a two-dimensional array of active elements.

We investigate collective behaviors in a two-dimensional array of active elements controlled by time-delayed feedback, where elements are prepared by localizing the Belousov-Zhabotinsky reaction in a gel matrix. We demonstrate that both the spatial and temporal coherence can be effectively controlled by varying feedback parameters, such as the time delay and the gain. For a sufficiently high feedback gain, the fully synchronized state with low temporal coherence appears, which might be the state induced only by the delay feedback. Experimental results are approximately reproduced in a numerical simulation with a forced Oregonator reaction-diffusion model.

Laser-controlled microscale fluid flows near the air-liquid interface of suspension droplets.

We investigate microscale flows of microparticles driven by a laser beam focused near the air-liquid interface of a suspension droplet. Three distinct regimes, convection, a linear flow, and a nonflow, are found by controlling both the position of the beam focus relative to the air-liquid interface and the laser power. They are governed by the most dominant of two effects exerted by a focused laser beam, i.e., local heating and radiation pressure. We find that in the nonflow regime two-dimensional close-packed arrays of microparticles are formed on the air-liquid interface, and spin on the beam axis. We show that micron-sized polystyrene beads can be bonded into a long chain structure by taking advantage of the linear flow.

Array-enhanced coherence resonance and phase synchronization in a two-dimensional array of excitable chemical oscillators.

We investigate the spatiotemporal dynamics in a two-dimensional array of excitable elements subjected to independent external noise, where elements are prepared by localizing the Belousov-Zhabotinsky reaction in a gel matrix. We experimentally demonstrate that the coherence of noise-induced firings is improved with increasing the array size, i.e., the occurrence of array-enhanced coherence resonance. Furthermore, it is found that synchronization among oscillators which are barely coupled can be achieved via coherence resonance. Experimental observations are approximately reproduced in a numerical simulation with a forced Oregonator reaction-diffusion model.

Successive splitting of autowaves in a nonlinear chemical reaction medium.

The phenomenon of wave splitting is investigated in a two-dimensional excitable light-sensitive Belousov-Zhabotinsky reaction medium after extremely changing the intensity of illuminated light for a short time. It is found that successive wave splitting and nonannihilation collision between two waves of different amplitudes occur spontaneously under narrow experimental conditions. Experimental observations are approximately reproduced in the specific parameter range by a numerical simulation with a Bär-Eiswirth model.

Noise-induced spatiotemporal dynamics in a linear array of excitable chemical oscillators.

The effects of additive noise on spatiotemporal dynamics are investigated in a one-dimensional array of excitable elements in which the Belousov-Zhabotinsky reaction is localized. At the appropriate separation between adjacent elements, we find that the resonance effect becomes larger for the element being more apart from the first element when only the first element is subjected to the external noise. This phenomenon is a sort of array-enhanced resonance. Furthermore, we find that phase locking between the first element and the other elements is induced via coherence resonance of the first element. Experimental observations are approximately reproduced in a numerical simulation with a forced Oregonator reaction-diffusion model.

Noise-induced phase locking in coupled coherence-resonance oscillators.

We investigate the effects of additive noise on coupled excitable chemical oscillators, particularly focusing on how oscillatory coupled modes can be induced by noise. We find that phase locking in the weak coupling regime occurs through coherence resonance, although the resulting phase locking modes are apparently similar to those in coupled deterministic oscillators. Experimental observations are approximately reproduced in a numerical simulation with a forced Oregonator reaction-diffusion model.

Dynamics of a stochastic oscillator in an excitable chemical reaction system.

Dynamics of an excitable Belousov-Zabotinsky reaction system subject to a subthreshold periodic signal and additive noise is investigated using cation exchange beads loaded with the cationic catalyst. We find two kinds of resonance phenomena with respect to the noise amplitude. At the first resonance, the regular oscillation appears with the period equal to the signal period, which is identified as a conventional stochastic resonance. The second resonance is a great contrast to conventional stochastic resonance, in which the regular oscillation appears in a characteristic fashion like phase locking of deterministic oscillators, depending on the signal period and a noise amplitude. Results are explained in terms of the interplay of periodic forcing and the noise-induced oscillator with the period determined by an intrinsic time scale of the system.

Experimental observation of coherence resonance in an excitable chemical reaction system.

Dynamics of an excitable Belousov-Zabotinsky reaction system under an external noise are investigated using cation exchange beads loaded with the cationic catalyst. When a noise amplitude is increased above a certain value, an oscillatory state appears. It is shown that the coherence of these noise-excited oscillations is maximal for a suitable value of the noise amplitude. This phenomenon is characterized by using various statistical measures, such as the signal-to-noise ratio in the power spectrum, the correlation time of the noise-excited oscillation, and the standard deviation of time intervals between successive firing events. We find the experimental evidence that the period of coherent oscillation is determined by a characteristic time scale of the system.

Noise-enhanced phase locking in a chemical oscillator system.

Dynamical responses of a chemical oscillator to an external electric field were investigated in the Belousov-Zabotinsky reaction system with the catalyst Ru(bpy)(3)(2+) [tris-(2,2(')-bipyridine) ruthenium (II)] immobilized in cation exchange beads. Periodic forcing above the threshold induced phase locking, whose synchronization region has a shape similar to the Arnold tongue. When a certain amount of noise together with a subthreshold periodic signal was imposed on the chemical oscillator, 1:1 phase locking to the periodic signal occurred. Its degree passed through a maximum with increase in the noise intensity, a manifestation of stochastic resonance in the form of noise-enhanced phase locking. The experimentally observed features were reproduced in a numerical simulation with a forced Oregonator reaction-diffusion model.