The synchronization of stochastic differential equations with linear noise

被引:5
作者
Al-Azzawi, Shahad Saadi Mahdi [1 ]
Liu, Jicheng [1 ]
Liu, Xianming [1 ]
机构
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China
关键词
Synchronization; random attractor; one-sided Lipschitz dissipative condition; linear noise; MULTIPLICATIVE NOISE; SYSTEMS; ATTRACTORS;
D O I
10.1142/S0219493718500491
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
The synchronization of stochastic differential equations with both additive noise and linear multiplicative noise is investigated in pathwise sense, which generalize the results of [5] and [6]. In our situation, we can deal with the synchronization of the systems with mixed type noise, where one system has the additive noise, another has the linear multiplicative noise.
引用
收藏
页数:31
相关论文
共 15 条
[1]   CONVERGENCE RATE OF SYNCHRONIZATION OF SYSTEMS WITH ADDITIVE NOISE [J].
Al-Azzawi, Shahad ;
Liu, Jicheng ;
Liu, Xianming .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (02) :227-245
[2]  
Arnold L., 1998, Random Dynamical Systems, V1
[3]   The persistence of synchronization under environmental noise [J].
Caraballo, T ;
Kloeden, PE .
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2005, 461 (2059) :2257-2267
[4]   Exponentially stable stationary solutions for stochastic evolution equations and their perturbation [J].
Caraballo, T ;
Kloeden, PE ;
Schmalfuss, B .
APPLIED MATHEMATICS AND OPTIMIZATION, 2004, 50 (03) :183-207
[5]   Synchronization of a stochastic reaction-diffusion system on a thin two-layer domain [J].
Caraballo, Tomas ;
Chueshov, Igor D. ;
Kloeden, Peter E. .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2007, 38 (05) :1489-1507
[6]   Synchronization of systems with multiplicative noise [J].
Caraballo, Tomas ;
Kloeden, Peter E. ;
Neuenkirch, Andreas .
STOCHASTICS AND DYNAMICS, 2008, 8 (01) :139-154
[7]   Upper semicontinuity of attractors and synchronization [J].
Carvalho, AN ;
Rodrigues, HM ;
Dlotko, T .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 220 (01) :13-41
[8]   The conjugacy of stochastic and random differential equations and the existence of global attractors [J].
Imkeller P. ;
Schmalfuss B. .
Journal of Dynamics and Differential Equations, 2001, 13 (2) :215-249
[9]   Nonautonomous attractors of switching systems [J].
Kloeden, P. E. .
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2006, 21 (02) :209-230
[10]  
Kloeden P.E., 2003, Elect. J. Dijf. Eqns, V1, P1