Multiscale Modeling &Simulation, Volume 18, Issue 3, Page 1343-1370, January 2020.
In this paper we consider systems of weakly interacting particles driven by colored noise in a bistable potential, and we study the effect of the correlation time of the noise on the bifurcation diagram for the equilibrium states. We accomplish this by solving the corresponding McKean--Vlasov equation using a Hermite spectral method, and we verify our findings using Monte Carlo simulations of the particle system. We consider both Gaussian and non-Gaussian noise processes, and for each model of the noise we also study the behavior of the system in the small correlation time regime using perturbation theory. The spectral method that we develop in this paper can be used for solving linear and nonlinear, local and nonlocal (mean field) Fokker--Planck equations, without requiring that they have a gradient structure.

中文翻译：

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具有彩色噪声的相互作用扩散的平均场极限：相变和光谱数值方法

2020年1月，《多尺度建模与仿真》，第18卷，第3期，第1343-1370页。
在本文中，我们考虑了由双稳态势中的有色噪声驱动的弱相互作用粒子系统，并且我们研究了噪声的相关时间对平衡状态的分叉图的影响。我们通过使用Hermite谱方法求解相应的McKean-Vlasov方程来完成此任务，并使用粒子系统的蒙特卡洛模拟来验证我们的发现。我们同时考虑了高斯噪声过程和非高斯噪声过程，并且对于每个噪声模型，我们还使用扰动理论研究了系统在小相关时间范围内的行为。我们在本文中开发的频谱方法可用于求解线性和非线性，局部和非局部（平均场）Fokker-Planck方程，而无需它们具有梯度结构。