Guoyong Yuan

Control of spiral-wave dynamics using feedback signals from line detectors

We numerically study trajectories of spiral-wave cores in excitable systems modulated proportionally to the integral of the activity on a straight line, several or dozens of equi-spaced measuring points on a straight line, a double line and a contour line. We show the single-line feedback results in the drift of core center along a straight line being parallel to the detector. An interesting finding is that the drift location in y is a piecewise linear increasing function of both the feedback line location and time delay. A similar trajectory occurs when replacing the feedback line with several or dozens of equi-spaced measuring points on the straight line. This allows to move the spiral core to the desired location along a chosen direction by measuring several or dozens of points. Under the double-line feedback, the shape of the tip trajectory representing the competition between the first and second feedback lines is determined by the distance of two lines. Various drift attractors in spiral wave controlled by square-shaped contour line feedback are also investigated. A brief explanation is presented.

Dynamics of pulses and spiral waves in excitable media with an anomalous diffusion

Spiral waves and pulses in the excitable medium with an anomalous diffusion are studied. In the medium with an one-sided fractional diffusion in the x-direction and a normal diffusion in the y-direction, a pulse, traveling along the positive x-direction, has a smaller velocity, which is different from the diffusion of a source in the other media. Its propagating velocity is a linear and increasing function of the square root of diffusion parameter, whose increasing rate depends on the fractional order. A minimal value of the diffusion parameter is needed for successfully propagating pulses, and the threshold becomes large with a decrease of the fractional order. For pulse trains, the frequency-locked bands are shifted along the increasing direction of the perturbation period when the fractional order is decreased. In the propagating process of a spiral wave, the tip drift is induced by the one-sided fractional diffusion, which may be explained by analyzing the SV area in front of the tip.

EFFECT OF EXTERNAL PERIODIC PULSES ON SPIRAL DYNAMICS AND CONTROL OF SPIRAL WAVES

In this paper, we study the effect of external periodic pulses on spiral dynamics. Resonant entrainment bands were observed on the period T-axis, and T is close to rational multiples of the path curvature period of the spiral tip on the bands. It is also shown that spiral waves are drifted and eliminated by applying the driving method with suitable control parameters, and we reveal the mechanism which forces the spiral wave to periodically shift and rotate. In the domain near the spiral tip, the bidirectional wave excitations are periodically generated by external pulses, and each excitation induces a straight drift of the spiral wave tip. Numerical results show that the parameter range of the external pulse period T, used to successfully eliminate spiral waves, is broaden by appropriately increasing the values of the pulse width and the amplitude. The low-amplitude control scheme is operable in many real systems, and its study is beneficial to understand the forced spiral dynamics.

Dynamics of meandering spiral waves under the modulation of a dichotomous noise

In this paper, we study the effect of a dichotomous noise on meandering spiral dynamics, and exhibit how the cycloid motion of the meandering spiral tip is destroyed by the noise. Switching on the noise does not alter the primary frequency f1 and the secondary frequency f2 in the tip motion, which is different from the case for a periodic dichotomous modulation, where f2 is changed according to two specific rules. However, the dichotomous noise leads to a decrease of the amplitudes at f1 and f2, and the rate of decrease of the amplitude at f2 is larger than that at f2 in the process of increasing the noise intensity or the correlation. The areas with small v-values (SV) are defined, and the distribution and size of the SV areas are analyzed, in order to explain and describe these results. It is also proved that spiral waves can be eliminated by the dichotomous noise with a large amplitude or correlation.