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.
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页码：875 / 887
页数：13
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