Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We aim to examine the most likely transition path between equilibrium stable states of the vector field. In the small noise regime, the action functional does not involve the solution of the skeleton equation which describes the unperturbed deterministic flow of the vector field shifted by the interaction at zero distance. As a result, we are led to study the most likely transition path for a stochastic differential equation without distribution dependency. This enables the computation of the most likely transition path for these distribution-dependent stochastic dynamical systems by the adaptive minimum action method and we illustrate our approach in two examples.

分布相关的随机动力系统广泛出现在工程和科学领域。我们考虑一类这样的系统，它模拟在随机波动的矢量场中移动的相互作用粒子的极限行为。我们的目标是检查矢量场平衡稳定状态之间最可能的过渡路径。在小噪声情况下，作用泛函不涉及骨架方程的解，该方程描述了因零距离相互作用而移动的矢量场的无扰动确定性流。因此，我们被引导去研究没有分布依赖性的随机微分方程最可能的转移路径。这使得能够通过自适应最小作用方法来计算这些依赖于分布的随机动力系统的最可能的转换路径，并且我们在两个示例中说明了我们的方法。