swarmalator系统中的有序、混沌与维度转变
Order, chaos, and dimensionality transition in a system of swarmalators
AI总结：
提出一种二维空间中可解的swarmalator模型，推导静态与主动集体态的出现条件，揭示多重稳定性及主动混沌态中的空间相关性变化与维度转变。
摘要：
与精子类似——其中个体在空间中自组织，同时也努力使其尾部摆动保持相干——若干自然和工程系统展现出群集与同步的涌现。这些现象的产生及相互作用已由被称为swarmalator（群集同步子）的假想粒子集合所刻画：每个粒子都具有位置和相位，其动力学受到彼此以及邻居空间-相位状态的相互影响。在本工作中，我们引入了一个可在二维空间中运动的可解swarmalator模型。我们展示了若干静态和主动的集体态能够涌现，并推导了随模型参数变化时每种状态出现的必要条件。在某些情况下，这些条件阐明了状态之间多重稳定性的呈现。值得注意的是，在主动区域中，个体表现出混沌行为，在某些条件下维持空间相关性，而在其他条件下则打破这种相关性，我们将其解释为一种维度转变。
英文摘要：
Similar to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of these phenomena have been captured by collectives of hypothetical particles named swarmalators, each possessing a position and a phase whose dynamics are affected reciprocally and also by the space-phase states of their neighbors. In this work, we introduce a solvable model of swarmalators able to move in two-dimensional spaces. We show that several static and active collective states can emerge and derive necessary conditions for each to show up as the model parameters are varied. These conditions elucidate, in some cases, the displaying of multistability among states. Notably, in the active regime, individuals behave chaotically, maintaining spatial correlation under certain conditions, and breaking it under others on what we interpret as a dimensionality transition.
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