Collective dynamics of swarmalators driven by a mobile pacemaker

Swarmalators, namely, oscillators with intrinsic frequencies that are able to self-propel to move in space, may undergo collective spatial swarming and meanwhile phase synchronous dynamics. In this paper, a swarmalator model driven by an external mobile pacemaker is proposed to explore the swarming dynamics in the presence of the competition between the external organization of the moving pacemaker and the intrinsic self-organization among oscillators. It is unveiled that the swarmalator system may exhibit a wealth of novel spatiotemporal patterns including the spindle state, the ripple state, and the trapping state. Transitions among these patterns and the mechanisms are studied with the help of different order parameters. The phase diagrams present systematic scenarios of various possible collective swarming dynamics and the transitions among them. The present study indicates that one may manipulate the formation and switching of the organized collective states by adjusting the external driving force, which is expected to shed light on applications of swarming performance control in natural and artificial groups of active agents.