AI 中文总结
该研究提出了一种由相位决定生死速率的马尔萨斯振子耦合机制，实现种群同步，将多频率类振子系统约化为常微分方程，是Kuramoto振子Ott–Antonsen约化的马尔萨斯类似物。
AI 中文摘要
振子种群通常因耦合将相位拉到一起而同步。这里我们考虑马尔萨斯振子，其耦合是人口统计学层面的：振子的出生和死亡速率由它们的相位决定，从而产生无相位速度相互作用的有效耦合。我们发现这种耦合可同步种群、选择集体频率，并产生非通用的四阶相干起始。这些集体动力学可实现精确约化：具有m个频率类的种群可约化为3m个常微分方程，这是Kuramoto振子的Ott–Antonsen约化的马尔萨斯类似物。
英文摘要
A population of oscillators typically synchronizes because coupling pulls their phases together. Here we consider malthusian oscillators whose coupling is demographic: oscillators are born and die at rates determined by their phases, generating an effective coupling without any phase velocity interaction. We find this coupling can synchronize a population, select a collective frequency, and produce a nongeneric fourth-root onset of coherence. These collective dynamics admit an exact reduction: a population with $m$ frequency classes reduces to $3m$ ordinary differential equations. This is the malthusian analogue of the Ott--Antonsen reduction for Kuramoto oscillators.
