标题： 群体振子中速度随时间变化的吸引-排斥挑战 显示英文标题

标题： Attractive-repulsive challenge in swarmalators with time-dependent speed

摘要： 我们研究了一个实体网络，其内部和外部动力学通过“swarmalators”这一概念紧密耦合，如O'Keeffe等人所引入的。 \textcolor{blue}{\cite{o2017oscillators}} 。 我们研究了实体的自然速度如何影响网络的集体动力学和同步路径。 具体来说，我们分析了两种情况：一种是每个实体都有一个单独的自然速度，另一种是群体速度由所有速度的平均值定义。 我们的发现揭示了两种不同的相位同步形式——静态和旋转——每种形式之前都伴随着实体之间吸引力和排斥力的复杂状态。 这种相互作用阶段对初始条件非常敏感，允许在网络中进行选择性调制。 通过调整初始参数，我们可以隔离特定的实体，使其在完全同步发生之前经历与群体不同的吸引力和排斥力相互作用。 这种对初始条件的细微依赖关系为自然速度在调节耦合动态网络中的同步行为方面的作用提供了有价值的见解。 显示英文摘要

摘要： We examine a network of entities whose internal and external dynamics are intricately coupled, modeled through the concept of ``swarmalators'' as introduced by O'Keeffe et al. \textcolor{blue}{\cite{o2017oscillators}}. We investigate how the entities' natural velocities impact the network's collective dynamics and path to synchronization. Specifically, we analyze two scenarios: one in which each entity has an individual natural velocity, and another where a group velocity is defined by the average of all velocities. Our findings reveal two distinct forms of phase synchronization -- static and rotational -- each preceded by a complex state of attractive-repulsive interactions between entities. This interaction phase, which depends sensitively on initial conditions, allows for selective modulation within the network. By adjusting initial parameters, we can isolate specific entities to experience attractive-repulsive interactions distinct from the group, prior to the onset of full synchronization. This nuanced dependency on initial conditions offers valuable insights into the role of natural velocities in tuning synchronization behavior within coupled dynamic networks.