Dynamical Behavior of Nonautonomous Stochastic Reaction-Diffusion Neural Network Models

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 - https://www.scopus.com/pages/publications/85054239060

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 -