A fundamental understanding of synchronized behavior in multiagent systems can be acquired by studying analytically tractable Kuramoto models. However, such models typically diverge from many real systems whose dynamics evolve under nonnegligible resource constraints. Here we construct a system of coupled Kuramoto oscillators that consume or produce resources as a function of their oscillation frequency. At high coupling, we observe strongly synchronized dynamics, whereas at low coupling, we observe independent oscillator dynamics as expected from standard Kuramoto models. For intermediate coupling, which typically induces a partially synchronized state, we empirically observe that (and theoretically explain why) the system can exist in either: (i) a state in which the order parameter oscillates in time, or (ii) a state in which multiple synchronization states are simultaneously stable. Whether (i) or (ii) occurs depends upon whether the oscillators consume or produce resources, respectively. Relevant for systems as varied as coupled neurons and social groups, our paper lays important groundwork for future efforts to develop quantitative predictions of synchronized dynamics for systems embedded in environments marked by sparse resources.

中文翻译：

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资源限制下耦合仓本振荡器的同步

通过研究易于分析的 Kuramoto 模型，可以获得对多智能体系统中同步行为的基本理解。然而，这些模型通常与许多真实系统不同，这些系统的动态在不可忽略的资源约束下发展。在这里，我们构建了一个耦合 Kuramoto 振荡器的系统，该系统根据其振荡频率消耗或产生资源。在高耦合时，我们观察到强同步动力学，而在低耦合时，我们观察到标准 Kuramoto 模型所预期的独立振荡器动力学。对于通常会导致部分同步状态的中间耦合，我们根据经验观察到（并在理论上解释了为什么）系统可以存在于以下任一状态：（i）顺序参数随时间振荡的状态，或 (ii) 多个同步状态同时稳定的状态。(i) 或 (ii) 是否发生取决于振荡器是否分别消耗或产生资源。与耦合神经元和社会群体等多种多样的系统相关，我们的论文为未来努力为嵌入在资源稀少的环境中的系统开发同步动力学的定量预测奠定了重要的基础。