Controlling the breakup of spiral waves in an excitable medium by applying time-delay feedback signals

– The spiral-wave breakup to turbulence in an excitable medium, starting from the spiral-wave center via Doppler instability, is controlled by modulating a local region around the spiral-wave center. The modulation signal is extracted from the controlled region with a certain time delay. By injecting a feedback signal with very low intensity into a very small space area, we can successfully stabilize the spiral wave and prevent breakup to turbulence. Spiral waves are frequently observed in a large variety of spatiotemporal systems [1–5]; often the features and the characteristic changes of the spiral waves are of crucial importance for practical purposes. For instance, the birth, death, and the transitions of spiral waves are closely related to the working conditions of animal hearts. Therefore, recently, the problem of spiral-wave control has attracted much attention [6–13]. There exist two major directions for the spiral-wave control: first, to kill spiral waves when they are harmful; second, to maintain well-behaved spiral waves in preventing them to break to spatiotemporal chaos. The former control problem has been investigated extensively [6–8], while the latter, which is extremely important in spiral-wave manipulation and pattern control, has been considered much less [9, 10]. In this letter we focus on the control of spiral-wave breakup (SWB). There are various kinds of SWBs, such as the breakup far from the spiral-wave center in an oscillatory medium due to the convective instability condition [2,11], and the one near the spiral-wave center in an excitable medium due to the absolute instability condition (Doppler instability) [5, 12]. Different approaches may be effective for controlling different SWBs in fitting the distinctive breakup mechanisms. In this letter, we focus on the SWB due to the Doppler mechanism in an excitable medium. Note that the heart system, which is one of the most important motivations for the study of spiral waves and spiral-wave control, is typically (∗) E-mail: [email protected]