The influence of spatiotemporal modulation on spiral tip dynamics in excitable medium and its application for spiral control

Abstract

In this paper, the influence of spatiotemporal modulation on tip dynamics of periodic spiral wave in excitable medium is studied first. By varying spatiotemporal modulation item, the dynamics of spiral wave changes dramatically and the system undergoes periodic spiral wave, epicycloid meandering spiral wave, traveling spiral wave and hypocycloid meandering spiral wave. An order parameter is introduced to detect the critical conditions of non-equilibrium transition between different patterns. And the variation of spiral tip radius induced by spatiotemporal modulation can also be reflected by this order parameter. When spatiotemporal modulation increases to a critical value, spiral waves break up. And spiral waves will damp to homogeneous rest state if spatiotemporal modulation increases further. The mechanisms of spiral breakup and damping are explained in the paper. Finally we apply the spatiotemporal modulation method to the meandering spiral waves and can successfully control meandering spiral waves into periodic spiral waves or homogeneous rest state.