TY - JOUR
T1 - Random Attractors for Fractional Stochastic Hindmarsh-Rose Equations with Memristors
AU - Xue, Renxiu
AU - Fu, Xianlong
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
PY - 2025/12
Y1 - 2025/12
N2 - In this paper, we devote to the study of dynamics of fractional stochastic Hindmarsh-Rose equations with memristors and multiplicative noises. We first apply the Galerkin method to prove the existence and uniqueness of the global solutions for the system under consideration. Then, based on some uniform estimates for the solutions we establish the existence and uniqueness of tempered pullback random attractors for the equations in an appropriate Hilbert space. Additionally, the upper semicontinuity of random attractors is also studied as the noise intensity approaches zero.
AB - In this paper, we devote to the study of dynamics of fractional stochastic Hindmarsh-Rose equations with memristors and multiplicative noises. We first apply the Galerkin method to prove the existence and uniqueness of the global solutions for the system under consideration. Then, based on some uniform estimates for the solutions we establish the existence and uniqueness of tempered pullback random attractors for the equations in an appropriate Hilbert space. Additionally, the upper semicontinuity of random attractors is also studied as the noise intensity approaches zero.
KW - Diffusive Hindmarsh-Rose equation
KW - Fractional Laplacian
KW - Multiplicative noise
KW - Random pullback attractor
UR - https://www.scopus.com/pages/publications/105024685041
U2 - 10.1007/s10883-025-09758-9
DO - 10.1007/s10883-025-09758-9
M3 - 文章
AN - SCOPUS:105024685041
SN - 1079-2724
VL - 31
JO - Journal of Dynamical and Control Systems
JF - Journal of Dynamical and Control Systems
IS - 4
M1 - 36
ER -