Perturbation theory for the Fokker-Planck operator in chaos

作者：Heninger, Jeffrey M.; Lippolis, Domenico^*; Cvitanovic, Predrag

来源：Communications in Nonlinear Science & Numerical Simulation, 2018, 55: 16-28.

DOI：10.1016/j.cnsns.2017.06.025

• Chaos
• Noise
• Fokker-Planck operator
• Perturbation theory
• Stationary distribution

The stationary distribution of a fully chaotic system typically exhibits a fractal structure, which dramatically changes if the dynamical equations are even slightly modified. Perturbative techniques are not expected to work in this situation. In contrast, the presence of additive noise smooths out the stationary distribution, and perturbation theory becomes applicable. We show that a perturbation expansion for the Fokker-Planck evolution operator yields surprisingly accurate estimates of long-time averages in an otherwise unlikely scenario.

• 出版日期2018-2
• 单位江苏大学