Stochastic systems with delay: Perturbation theory for second order statistics

被引：5

作者：

Frank, T. D. ^{[1
,2
]}

机构：

[1] Univ Connecticut, Dept Psychol, Storrs, CT 06269 USA

[2] Univ Connecticut, Dept Phys, Storrs, CT 06269 USA

来源：

PHYSICS LETTERS A | 2016年 / 380卷 / 14-15期

关键词：

Delay; Autocorrelation function; Fokker-Planck equation; INDUCED TRANSITIONS; STATE TRANSITIONS; TIME-DELAY; NOISE; OSCILLATIONS; BISTABILITY; DYNAMICS; DEFECTS; MODEL; CHAOS;

D O I：

10.1016/j.physleta.2016.02.011

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Within the framework of delay Fokker-Planck equations, a perturbation theoretical method is developed to determine second-order statistical quantities such as autocorrelation functions for stochastic systems with delay. Two variants of the perturbation theoretical approach are presented. The first variant is based on a non-local Fokker-Planck operator. The second variant requires to solve a Fokker-Planck equation with source term. It is shown that the two variants yield consistent results. The perturbation theoretical approaches are applied to study negative autocorrelations that are induced by feedback delays and mediated by the strength of the fluctuating forces that act on the feedback systems. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：1341 / 1351

页数：11

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