Allawala Altan, Marston J B
Department of Physics, Box 1843, Brown University, Providence, Rhode Island 02912-1893, USA.
Phys Rev E. 2016 Nov;94(5-1):052218. doi: 10.1103/PhysRevE.94.052218. Epub 2016 Nov 23.
We investigate the Fokker-Planck description of the equal-time statistics of the three-dimensional Lorenz attractor with additive white noise. The invariant measure is found by computing the zero (or null) mode of the linear Fokker-Planck operator as a problem of sparse linear algebra. Two variants are studied: a self-adjoint construction of the linear operator and the replacement of diffusion with hyperdiffusion. We also access the low-order statistics of the system by a perturbative expansion in equal-time cumulants. A comparison is made to statistics obtained by the standard approach of accumulation via direct numerical simulation. Theoretical and computational aspects of the Fokker-Planck and cumulant expansion methods are discussed.
我们研究了具有加性白噪声的三维洛伦兹吸引子等时统计量的福克 - 普朗克描述。通过将线性福克 - 普朗克算子的零（或空）模计算为一个稀疏线性代数问题来找到不变测度。研究了两种变体：线性算子的自伴构造以及用超扩散替代扩散。我们还通过等时累积量的微扰展开来获取系统的低阶统计量。并与通过直接数值模拟的标准累积方法获得的统计量进行了比较。讨论了福克 - 普朗克方法和累积量展开方法的理论及计算方面。
