Dynamics of spiral wave chimeras subjected to a local feedback control

The response of the spiral wave chimera on the feedback signal from a measuring location is investigated in the three-component reaction–diffusion system with two spatial dimensions. When the feedback gain is small, the feedback forces the incoherent core to follow a circular orbit with finger-shaped bulges, and the circular path exhibits more complex structures with an increases of the time delay. For a large feedback gain, the excitation in front of the wave front causes the disappearance of the spiral arm except for some residual segments, which will be developed into the wave structures with multiple incoherent cores, where one of the cores is located at the measuring point. Four types of dynamical behaviors are identified for an intermediate feedback gain, depending on the time delay, and these behaviors cannot be observed in the local feedback control of normal spiral waves. For the first three types, the spiral chimera will eventually disappear, but through three different processes, including the formation of transient incoherent arcs, the drift of the incoherent core to the boundary along a spiral, and the complex drift with a transient closed path. The fourth type appears for a large time delay, where the incoherent core drifts to the measuring point along a spiral. These results relate to the control of the spiral chimera, where the spiral chimera can be eliminated by the feedback exhibiting the first three dynamical behaviors, and its core can be controlled to the designated location by the feedback exhibiting the fourth dynamical behavior.