非自治分数阶随机Hindmarsh-Rose方程的随机吸引子  

Random attractors of non-autonomous fractional stochastic Hindmarsh-Rose equations

作　　者：盛焕义 刘辉 辛杰[1,2] SHENG Huanyi;LIU Hui;XIN Jie(School of Mathematical Sciences,Qufu Normal University,273165,Qufu;College of Information Science and Engineering,Shandong Agricultural University,271018,Taian,Shandong,PRC)

机构地区：[1]曲阜师范大学数学科学学院,曲阜市273165 [2]山东农业大学信息科学与工程学院,山东省泰安市271018

出　　处：《曲阜师范大学学报（自然科学版）》2022年第3期103-113,共11页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(11371183);山东省自然科学基金(ZR2013AM004,ZR2018QA002).

摘　　要：该文将带有乘性白噪声项的非自治随机Hindmarsh-Rose方程中的标准拉普拉斯算子改变成分数阶拉普拉斯算子,并将这一方程组转换为向量形式,然后引用伽略金方法证明了一类由乘性噪声驱动的非自治分数阶Hindmarsh-Rose方程解的存在性和唯一性.最后在适当的Hilbert空间中建立了这些方程的调和拉回吸引子的存在性和唯一性.This paper changes the standard Laplacian in the non-autonomous stochastic Hindmarsh-Rose equation with a multiplicative white noise term into a fractional Laplacian,and converts this system of equations into vector form.Then Galerkin’s method is used to prove the existence and uniqueness of solutions for a class of non-autonomous fractional Hindmarsh-Rose equations driven by multiplicative noise.Finally,the existence and uniqueness of tempered pullback random attractors for the equations are established in an appropriate Hilbert space.

关 键 词：随机吸引子 分数阶随机方程 拉回渐近紧性 

分 类 号：O241.8[理学—计算数学]