Design and application of feedback-sustained target waves in excitable medium

In this paper, we present a formulas of rational ratios between the frequency of external stimulus and its paced target waves, considering the existence of the absolute refractory period and the relative refractory period. Based on this, we design a self-sustained high-frequency target waves by feeding back few periphery field points to the center to responsibly play the role of source for pacemaker. Such constructed target waves, to all appearances, are shown as a repetition of their initial condition. We explore further in application that those feedback-sustained targets can eliminate both a freely rotating spiral waves and a pinned ones only if frequencies, feedback lengths and radius of obstacles are appropriately chosen. After feedback stimuli are removed, the system eventually returns to the rest state.

► We give a formula of the frequency of pacing stimuli and target waves.
► A self-sustained target wave is constructed by feeding back points to the center.
► Feedback-sustained targets can control a freely rotating or a pinned spiral wave.