Li Kuan, Marston J B, Saxena Saloni, Tobias Steven M
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom.
Department of Physics, Brown University, Box 1843, Providence, Rhode Island 02912-1843, USA.
Chaos. 2022 Apr;32(4):043111. doi: 10.1063/5.0075580.
We use direct statistical simulation to find the low-order statistics of the well-known dynamical system, the Lorenz63 model. Instead of accumulating statistics from numerical simulation of the dynamical system or solving the Fokker-Planck equation for the full probability distribution of the dynamical system, we directly solve the equations of motion for the low-order statistics after closing them by making several different choices for the truncation. Fixed points of the statistics are obtained either by time evolving or by iterative methods. The stability and statistical realizability of the fixed points of the statistics are analyzed, and the statistics so obtained are compared to those found by the traditional approach. Low-order statistics of the chaotic Lorenz63 system can be obtained from cumulant expansions more efficiently than by accumulation via direct numerical simulation or by solution of the Fokker-Planck equation.
我们使用直接统计模拟来寻找著名动力系统——洛伦兹63模型的低阶统计量。我们并非通过动力系统的数值模拟来累积统计量，也不是求解动力系统全概率分布的福克 - 普朗克方程，而是在进行几种不同截断选择以封闭方程后，直接求解低阶统计量的运动方程。统计量的不动点可通过时间演化或迭代方法获得。我们分析了统计量不动点的稳定性和统计可实现性，并将如此获得的统计量与传统方法得到的统计量进行比较。混沌洛伦兹63系统的低阶统计量可通过累积量展开比通过直接数值模拟累积或求解福克 - 普朗克方程更有效地获得。
