标题： 具有高阶相互作用的二维swarmalator模型 显示英文标题

标题： A two-dimensional swarmalator model with higher-order interactions

摘要： 我们研究了一个简单的二维swarmalator模型，该模型结合了高阶相位相互作用，揭示了一系列集体状态。 后者包括空间上连贯和气体状的构型，这些构型在只有二元相互作用的模型中并未出现。 此外，我们还发现了各种状态之间的双稳态现象，这一现象直接源于高阶相互作用的引入。 通过分析这些涌现状态中的几个状态（对于相同的和不同的swarmalator群体），我们获得了对其潜在机制和稳定性条件的更深入理解。 我们的发现扩展了对swarmalator动力学的理解，并为探索受高阶相互作用支配的系统的复杂集体行为开辟了新的途径。 显示英文摘要

摘要： We study a simple two-dimensional swarmalator model that incorporates higher-order phase interactions, uncovering a diverse range of collective states. The latter include spatially coherent and gas-like configurations, neither of which appear in models with only pairwise interactions. Additionally, we discover bistability between various states, a phenomenon that arises directly from the inclusion of higher-order interactions. By analyzing several of these emergent states analytically, both for identical and nonidentical populations of swarmalators, we gain deeper insights into their underlying mechanisms and stability conditions. Our findings broaden the understanding of swarmalator dynamics and open new avenues for exploring complex collective behaviors in systems governed by higher-order interactions.