TY - JOUR
T1 - Dynamical Behavior of Nonautonomous Stochastic Reaction-Diffusion Neural Network Models
AU - Wei, Tengda
AU - Lin, Ping
AU - Zhu, Quanxin
AU - Wang, Linshan
AU - Wang, Yangfan
N1 - This work was supported in part
by the National Natural Science Foundation of China under Grant 11771014,
Grant 61773217, Grant 61374080, and Grant 91430106, in part by the
Natural Science Foundation of Jiangsu Province under Grant BK20161552,
in part by the Alexander von Humboldt Foundation of Germany under
Grant CHN/1163390, in part by the Fundamental Research Funds for the
Central Universities under Grant 06500073, and in part by the China
Scholarship Council under Grant 201706330011. (Corresponding authors:
Ping Lin; Yangfan Wang.)
PY - 2019/5
Y1 - 2019/5
N2 - This brief investigates nonautonomous stochastic reaction-diffusion neural-network models with S-type distributed delays. First, the existence and uniqueness of mild solution are studied under the Lipschitz condition without the linear growth condition. Due to the existence of a nonautonomous reaction-diffusion term and the infinite dimensional Wiener process, the criteria for the well-posedness of the models are established based on the evolution system theory. Then, the S-type distributed delay, which is an infinite delay, is handled by the truncation method, and sufficient conditions for the global exponential stability are obtained by constructing a simple Lyapunov-Krasovskii functional candidate. Finally, neural-network examples and an illustrative example are given to show the applications of the obtained results.
AB - This brief investigates nonautonomous stochastic reaction-diffusion neural-network models with S-type distributed delays. First, the existence and uniqueness of mild solution are studied under the Lipschitz condition without the linear growth condition. Due to the existence of a nonautonomous reaction-diffusion term and the infinite dimensional Wiener process, the criteria for the well-posedness of the models are established based on the evolution system theory. Then, the S-type distributed delay, which is an infinite delay, is handled by the truncation method, and sufficient conditions for the global exponential stability are obtained by constructing a simple Lyapunov-Krasovskii functional candidate. Finally, neural-network examples and an illustrative example are given to show the applications of the obtained results.
KW - Existence-uniqueness and stability
KW - S-type delay.
KW - mild solution
KW - reaction-diffusion
KW - stochastic neural network
UR - http://www.scopus.com/inward/record.url?scp=85054239060&partnerID=8YFLogxK
U2 - 10.1109/TNNLS.2018.2869028
DO - 10.1109/TNNLS.2018.2869028
M3 - Article
C2 - 30273158
SN - 2162-237X
VL - 30
SP - 1575
EP - 1580
JO - IEEE Transactions on Neural Networks and Learning Systems
JF - IEEE Transactions on Neural Networks and Learning Systems
IS - 5
ER -
