Dynamics and control of spiral waves under feedback derived from a moving measuring point

Abstract

Feedback control of spiral waves by the signal derived from a moving measuring point is investigated in the two-dimensional FitzHugh–Nagumo model, where the measuring location is changed with the motion of the spiral tip according to two schemes. In the first scheme, the direction of the line joining the spiral tip and the moving measuring point at the same time remains unchanged during the feedback control, and the application of the feedback signal can make the spiral tip gradually drift to the non-flux boundary of the system, which eventually causes the disappearance of the whole spiral pattern. It is interesting that the drift unit can always travel in a straight line after a period of time, which is more effective for eliminating spiral waves. The direction angles of the straight drift and the initial drift depend on the parameters for determining the measuring location. The second scheme is designed to has a fixed included angle between the joining line and the tangent line of the tip path at the instantaneous tip position during the control. In response to the feedback control, the system can show a few types of dynamical behaviors, including the transition from the inward-petal to outward-petal tip paths, the shrinkage of the attractor region for outward-petal tip paths with a larger unexcited core, and the transition from meandering to rigidly rotating spirals.