THE MEAN-SQUARE DICHOTOMY SPECTRUM AND A BIFURCATION TO A MEAN-SQUARE ATTRACTOR

被引：7

作者：

Doan, Thai Son ^{[1
,3
]}

Rasmussen, Martin ^{[1
]}

Kloeden, Peter E. ^{[2
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[3] Vietnam Acad Sci & Technol, Inst Math, Hanoi, Vietnam

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2015年 / 20卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Dichotomy spectrum; mean-square random dynamical system; mean-square random attractor; bifurcation;

D O I：

10.3934/dcdsb.2015.20.875

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact intervals. It is then demonstrated that a change in the sign of the dichotomy spectrum is associated with a bifurcation from a trivial to a non-trivial mean-square random attractor.

引用

页码：875 / 887

页数：13

共 13 条

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Kloeden, Peter E.
Marin-Rubio, Pedro
[J]. SET-VALUED AND VARIATIONAL ANALYSIS, 2011, 19 (01) : 43 - 57
[10] Stochastic Differential Equations with Nonlocal Sample Dependence
Kloeden, Peter E.
Lorenz, Thomas
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2010, 28 (06) : 937 - 945

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