标题： 拓扑状态和无力互惠的swarmalators连续体模型 显示英文标题

标题： Topological states and continuum model for swarmalators without force reciprocity

摘要： 群体振子是既具有自推进粒子特性又具有振荡器特性的系统。 每个粒子都具有一个相位，该相位调节其与其他粒子之间的相互作用力。 反过来，相对位置调节相互作用粒子之间的相位同步。 在目前的模型中，不存在力的互易性：当一个粒子吸引另一个粒子时，后者会排斥前者。 这导致了追逐行为。 在本文中，我们推导了这种群体振子系统的流体动力学模型，并表明它在二维空间中具有显式的双周期行波解。 这些特殊解具有非平凡的拓扑结构，其拓扑性质由沿任一维度周期内的相位矢量指标来量化。 通过研究模型的双曲性条件，研究了这些解的稳定性。 展示了粒子模型和流体动力学模型的数值解。 它们证实了流体动力学模型在小时间或大相位噪声情况下的粒子模型一致性，同时也揭示了在小相位噪声情况下出现的引人入胜的模式。 显示英文摘要

摘要： Swarmalators are systems of agents which are both self-propelled particles and oscillators. Each particle is endowed with a phase which modulates its interaction force with the other particles. In return, relative positions modulate phase synchronization between interacting particles. In the present model, there is no force reciprocity: when a particle attracts another one, the latter repels the former. This results in a pursuit behavior. In this paper, we derive a hydrodynamic model of this swarmalator system and show that it has explicit doubly-periodic travelling-wave solutions in two space dimensions. These special solutions enjoy non-trivial topology quantified by the index of the phase vector along a period in either dimension. Stability of these solutions is studied by investigating the conditions for hyperbolicity of the model. Numerical solutions of both the particle and hydrodynamic models are shown. They confirm the consistency of the hydrodynamic model with the particle one for small times or large phase-noise but also reveal the emergence of intriguing patterns in the case of small phase-noise.