We consider a red-versus-blue coupled synchronization and spatial swarming (i.e., swarmalator) model that incorporates attraction and repulsion terms and an adversarial game of phases. The model exhibits behaviors such as spontaneous emergence of tactical manoeuvres of envelopment (e.g., flanking, pincer, and envelopment) that are often proposed in military theory or observed in nature. We classify these states based on a large set of features such as spatial densities, synchronization between clusters, and measures of cluster distances. These features are used to study the influence of coupling parameters on the expected presence of these states and the—sometimes sharp—transitions between them.

中文翻译：

---

对抗性同步与群体模型中的突发行为

我们考虑了一个红色对蓝色耦合的同步和空间群（即Swarmalator）模型，该模型结合了吸引和排斥项以及对抗性的阶段博弈。该模型展示了一些行为，例如在军事理论中经常提出或在自然界中经常观察到的诸如包围战术战术（例如侧翼，钳子和包围）的自发出现。我们基于大量特征（例如空间密度，群集之间的同步以及群集距离的度量）对这些状态进行分类。这些特征用于研究耦合参数对这些状态的预期存在以及它们之间（有时是急剧的）转变的影响。