A wide variety of biological phenomena can be modeled by the collective activity of a population of individual units. A common strategy for simulating such a system, the population density approach, is to take the macroscopic limit and update its population density function. However, in many cases, the coupling between the units and noise gives rise to complex behaviors challenging to existing population density approach methods. To address these challenges, we develop the asymmetric particle population density (APPD) method that efficiently and accurately simulates such populations consist of coupled elements. The APPD is well-suited for a parallel implementation. We compare the performance of the method against direct Monte-Carlo simulation and verify its accuracy by applying it to the well-studied Hodgkin-Huxley model, with a range of challenging scenarios. We find that our method can accurately reproduce complex macroscopic behaviors such as inhibitory coupling-induced clustering and noise-induced firing while being faster than the direct simulation.

中文翻译：

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用于模拟耦合噪声振荡器的非对称粒子群密度方法

可以通过单个单元群体的集体活动来模拟各种各样的生物现象。模拟这种系统的常用策略，即人口密度方法，是取宏观极限并更新其人口密度函数。然而，在许多情况下，单元和噪声之间的耦合会产生复杂的行为，对现有的人口密度方法提出挑战。为了应对这些挑战，我们开发了非对称粒子群密度 (APPD) 方法，该方法可以高效准确地模拟由耦合元素组成的此类群。APPD 非常适合并行实现。我们将该方法的性能与直接蒙特卡罗模拟进行比较，并通过将其应用于经过充分研究的 Hodgkin-Huxley 模型来验证其准确性，具有一系列具有挑战性的场景。我们发现我们的方法可以准确地再现复杂的宏观行为，例如抑制耦合诱导的聚类和噪声诱导的触发，同时比直接模拟更快。