Noisy homoclinic pulse dynamics

被引：3

作者：

Eaves, T. S. ^{[1
]}

Balmforth, Neil J. ^{[2
]}

机构：

[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Wilberforce Rd, Cambridge CB3 0WA, England

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

来源：

CHAOS | 2016年 / 26卷 / 04期

基金：

美国国家科学基金会;

关键词：

HETEROCLINIC CYCLES; ORBITS; BIFURCATIONS; MODEL; MAPS;

D O I：

10.1063/1.4945794

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The effect of stochastic perturbations on nearly homoclinic pulse trains is considered for three model systems: a Duffing oscillator, the Lorenz-like Shimizu-Morioka model, and a co-dimension-three normal form. Using the Duffing model as an example, it is demonstrated that the main effect of noise does not originate from the neighbourhood of the fixed point, as is commonly assumed, but due to the perturbation of the trajectory outside that region. Singular perturbation theory is used to quantify this noise effect and is applied to construct maps of pulse spacing for the Shimizu-Morioka and normal form models. The dynamics of these stochastic maps is then explored to examine how noise influences the sequence of bifurcations that take place adjacent to homoclinic connections in Lorenzlike and Shilnikov-type flows. (C) 2016 AIP Publishing LLC.

引用

页数：11

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