The asymmetric particle population density method for simulation of coupled noisy oscillators

Abstract

Many 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 track a population density function. Here, we develop the asymmetric particle population density (APPD) method that efficiently and accurately simulates populations with complex behaviors that are infeasible for previous population density-based methods. The APPD method is well-suited for a parallel implementation. 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. We compare the method's performance 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.