Attractive - repulsive challenge in swarmalators with time - dependent speed

In this work, we consider a network of entities whose internal dynamics are coupled to their external dynamics. Using this system, called swarmalators introduced by O'Keeffe et al, we highlight the influence of the natural velocities of the entities on the overall dynamics on the way to synchronization of the network. We consider in one case an individual natural velocity and in the other a group velocity resulting from the average of the velocities. We obtain static and rotational phase synchronization preceded by a state of attractive-repulsive challenge between the entities. The dependence of this challenge to the initial conditions was analyzed and revealed that, we can change the elements that can exhibit attractive-repulsive challenge from the rest of the group before reaching synchronization.