Kroma-Wiley Keith A, Mucha Peter J, Bassett Danielle S
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Department of Mathematics and Department of Applied Physical Sciences, University of North Carolina, Chapel Hill, North Carolina 27599, USA.
Phys Rev E. 2021 Jul;104(1-1):014211. doi: 10.1103/PhysRevE.104.014211.
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.
通过研究易于进行分析处理的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，此类模型通常与许多实际系统不同，这些实际系统的动力学在不可忽略的资源约束下演化。在此，我们构建了一个耦合Kuramoto振子系统，该系统根据其振荡频率消耗或产生资源。在强耦合时，我们观察到强同步动力学，而在弱耦合时，我们观察到如标准Kuramoto模型所预期的独立振子动力学。对于通常会诱导部分同步状态的中间耦合，我们通过实验观察到（并从理论上解释了原因）系统可以存在于以下两种状态之一：（i）序参量随时间振荡的状态，或（ii）多个同步状态同时稳定的状态。出现（i）还是（ii）分别取决于振子是消耗还是产生资源。我们的论文对于耦合神经元和社会群体等各种系统具有相关性，为未来努力开发对嵌入资源稀缺环境中的系统同步动力学进行定量预测奠定了重要基础。
